6: digital representation of analog signals · 5 summary 6: digital representation of analog...
TRANSCRIPT
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
6: Digital Representation of Analog Signals
Y. Yoganandam, Runa Kumari, and S. R. Zinka
Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus
Sep 16 – Sep 24, 2015
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Outline
1 Sampling Theorem
2 Pulse Code Modulation
3 Differential Pulse Code Modulation
4 Delta Modulation
5 Summary
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Outline
1 Sampling Theorem
2 Pulse Code Modulation
3 Differential Pulse Code Modulation
4 Delta Modulation
5 Summary
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
g(t)
t0
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
g(t)
t0
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 6: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/6.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
g(t)
t0
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 7: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/7.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
g(t)
t0
0
G(f)
f
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 8: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/8.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
g(t)
t0
0
G(f)
f
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 9: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/9.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 10: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/10.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
We obtain sampled signal g (t) by multiplying g (t) with impulse train δTs (t).Impulse train can be expressed as a Fourier series as shown below:
δTs (t) =1Ts
[1 + 2 cos ωst + 2 cos 2ωst + 2 cos 3ωst + · · · ] , ωs =2π
Ts
Therefore
g (t) = g (t) δTs (t)
=1Ts
[g (t) + 2g (t) cos ωst + 2g (t) cos 2ωst + 2g (t) cos 3ωst + · · · ] .
Applying Fourier transform on both sides of the above equation gives
G (ω) =1Ts
∞
∑n=−∞
G (ω− nωs) . (1)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
We obtain sampled signal g (t) by multiplying g (t) with impulse train δTs (t).Impulse train can be expressed as a Fourier series as shown below:
δTs (t) =1Ts
[1 + 2 cos ωst + 2 cos 2ωst + 2 cos 3ωst + · · · ] , ωs =2π
Ts
Therefore
g (t) = g (t) δTs (t)
=1Ts
[g (t) + 2g (t) cos ωst + 2g (t) cos 2ωst + 2g (t) cos 3ωst + · · · ] .
Applying Fourier transform on both sides of the above equation gives
G (ω) =1Ts
∞
∑n=−∞
G (ω− nωs) . (1)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 12: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/12.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
We obtain sampled signal g (t) by multiplying g (t) with impulse train δTs (t).Impulse train can be expressed as a Fourier series as shown below:
δTs (t) =1Ts
[1 + 2 cos ωst + 2 cos 2ωst + 2 cos 3ωst + · · · ] , ωs =2π
Ts
Therefore
g (t) = g (t) δTs (t)
=1Ts
[g (t) + 2g (t) cos ωst + 2g (t) cos 2ωst + 2g (t) cos 3ωst + · · · ] .
Applying Fourier transform on both sides of the above equation gives
G (ω) =1Ts
∞
∑n=−∞
G (ω− nωs) . (1)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 13: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/13.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
We obtain sampled signal g (t) by multiplying g (t) with impulse train δTs (t).Impulse train can be expressed as a Fourier series as shown below:
δTs (t) =1Ts
[1 + 2 cos ωst + 2 cos 2ωst + 2 cos 3ωst + · · · ] , ωs =2π
Ts
Therefore
g (t) = g (t) δTs (t)
=1Ts
[g (t) + 2g (t) cos ωst + 2g (t) cos 2ωst + 2g (t) cos 3ωst + · · · ] .
Applying Fourier transform on both sides of the above equation gives
G (ω) =1Ts
∞
∑n=−∞
G (ω− nωs) . (1)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 14: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/14.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
If we are to reconstruct g (t) from g (t), we should be able to recover G (ω)from G (ω) . It is possible only when
1Ts
> 2B. (2)
The above equation can be rewritten as
fs > 2B, (3)
where, fs = 1/Ts, is the sampling frequency.
So, as long as fs is greater than twice the signal bandwidth B, we can recoverthe original signal g (t). The minimum sampling frequency fs = 2B requiredto recover g (t) is called Nyquist rate.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
If we are to reconstruct g (t) from g (t), we should be able to recover G (ω)from G (ω) . It is possible only when
1Ts
> 2B. (2)
The above equation can be rewritten as
fs > 2B, (3)
where, fs = 1/Ts, is the sampling frequency.
So, as long as fs is greater than twice the signal bandwidth B, we can recoverthe original signal g (t). The minimum sampling frequency fs = 2B requiredto recover g (t) is called Nyquist rate.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
If we are to reconstruct g (t) from g (t), we should be able to recover G (ω)from G (ω) . It is possible only when
1Ts
> 2B. (2)
The above equation can be rewritten as
fs > 2B, (3)
where, fs = 1/Ts, is the sampling frequency.
So, as long as fs is greater than twice the signal bandwidth B, we can recoverthe original signal g (t). The minimum sampling frequency fs = 2B requiredto recover g (t) is called Nyquist rate.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 17: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/17.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem
If we are to reconstruct g (t) from g (t), we should be able to recover G (ω)from G (ω) . It is possible only when
1Ts
> 2B. (2)
The above equation can be rewritten as
fs > 2B, (3)
where, fs = 1/Ts, is the sampling frequency.
So, as long as fs is greater than twice the signal bandwidth B, we can recoverthe original signal g (t). The minimum sampling frequency fs = 2B requiredto recover g (t) is called Nyquist rate.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 25: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/25.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Zero-Order Hold Circuit
g(t)
t0
0
G(f)
f
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS-1/2TS +1/2TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS-1/2TS +1/2TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS-1/2TS +1/2TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS-1/2TS +1/2TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS-1/2TS +1/2TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal Reconstruction – Ideal Interpolation
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS-1/2TS +1/2TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Issues with Sampling
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling Rate
G(f)
f0-2/TS -1/TS 2/TS1/TS
Smaller sampling rate
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling Rate
G(f)
f0-2/TS -1/TS 2/TS1/TS
Smaller sampling rate
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling Rate
G(f)
f0-2/TS -1/TS 2/TS1/TS
0
G(f)
f1/TS-2/TS -1/TS 2/TS
Smaller sampling rate
Larger sampling rate
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Lowpass Filtering – Ideal
0
G(f)
f1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Lowpass Filtering – Ideal
0
G(f)
f1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Lowpass Filtering – Still Ideal
0
G(f)
f1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Lowpass Filtering – Practical
0
G(f)
f1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Aliasing (Spectral Folding)
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Aliasing (Spectral Folding)
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Aliasing (Spectral Folding)
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Aliasing (Spectral Folding)
0
G(f)
f1/TS
Lost tailLost tail getsfolded back
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Aliasing (Spectral Folding)
0
G(f)
f1/TS-2/TS -1/TS 2/TS
Lost tailLost tail getsfolded back
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Aliasing (Spectral Folding)
0
G(f)
f1/TS-2/TS -1/TS 2/TS
Lost tailLost tail getsfolded back
Recoveredspectrum
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Antialiasing Filter
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Antialiasing Filter
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Antialiasing Filter
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Antialiasing Filter
0
G(f)
f
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Antialiasing Filter
0
G(f)
f1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Antialiasing Filter
What happens if we implement antialiasing filter after sampling?
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling
g(t)
t0
TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Practical Sampling
g(t)
t0
0
G(f)
f
TS
1/TS-2/TS -1/TS 2/TS
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Applications of Sampling Theorem
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
PAM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
PAM
PWM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
PAM
PWM
PPM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
Time division multiplexing
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
Ch. 3
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Sampling Theorem – Applications
CoderDigital
processor
Transmissionmedium
Digitalprocessor Decoder
Channel
Channel
LPF
LPF
LPF
LPF
1
23
2
24
1
23
2
24
Coder output(pulse code)
Ch. 1
Ch. 2
Ch. 4
Ch. 5
Ch. 3Ch. 6
Ch. 7
Ch. 24
Ch. 1
Ch. 2
Ch. 3
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Outline
1 Sampling Theorem
2 Pulse Code Modulation
3 Differential Pulse Code Modulation
4 Delta Modulation
5 Summary
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Analog vs Digital & Continuous vs Discrete
PCM is a method of converting an analog signal into digital signal (A/Dconversion).
In order to understand PCM, understanding the difference among the termsanalog, digital, continuous, and discrete is very very important.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Analog vs Digital & Continuous vs Discrete
PCM is a method of converting an analog signal into digital signal (A/Dconversion).
In order to understand PCM, understanding the difference among the termsanalog, digital, continuous, and discrete is very very important.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Analog vs Digital & Continuous vs Discrete
PCM is a method of converting an analog signal into digital signal (A/Dconversion).
In order to understand PCM, understanding the difference among the termsanalog, digital, continuous, and discrete is very very important.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Continuous Analog Signal
x(t)
1234567
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Discrete Analog Signal
x(t)
1234567
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Discrete (8-ary) Digital Signal
x(t)
1234567
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Continuous (8-ary) Digital Signal
x(t)
1234567
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Continuous Digital Signal – Binary PCM
x(t)
1234567
t000 100 101 100 011 100 110 111 101 011 011 100 100
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Code Modulation (PCM) – Trivia
Even though PCM is invented as early as 1926, It was the transistor thatmade PCM practicable in early 60s.
Average power of a PCM signal is less. However, the price paid is theincrease in the signal bandwidth.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Code Modulation (PCM) – Trivia
Even though PCM is invented as early as 1926, It was the transistor thatmade PCM practicable in early 60s.
Average power of a PCM signal is less. However, the price paid is theincrease in the signal bandwidth.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 90: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/90.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Code Modulation (PCM) – Trivia
Even though PCM is invented as early as 1926, It was the transistor thatmade PCM practicable in early 60s.
Average power of a PCM signal is less. However, the price paid is theincrease in the signal bandwidth.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 91: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/91.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
PCM– Steps Involved
1 Sampling
2 Quantization
3 Encoding
4 Baseband transmission (we will discuss this topic in next chapter)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
PCM– Steps Involved
1 Sampling
2 Quantization
3 Encoding
4 Baseband transmission (we will discuss this topic in next chapter)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 93: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/93.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
PCM– Steps Involved
1 Sampling
2 Quantization
3 Encoding
4 Baseband transmission (we will discuss this topic in next chapter)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
PCM– Steps Involved
1 Sampling
2 Quantization
3 Encoding
4 Baseband transmission (we will discuss this topic in next chapter)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
PCM– Steps Involved
1 Sampling
2 Quantization
3 Encoding
4 Baseband transmission (we will discuss this topic in next chapter)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 96: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/96.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
mp
-mp
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
mp
-mp
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
mp
-mp
2mp
L
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
mp
-mp
2mp
L
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization
m(t)
t
m(t)>
mp
-mp
2mp
L
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization Error
Quantization error is defined as
q (t) = m (t)−m (t). (4)
From the figure shown in the previous slide,
−∆v/2 ≤ q (t) ≤ ∆v/2, (5)
where∆v = 2mp/L.
Assuming that the error is equally likely to lie anywhere in the range(−∆v/2,+∆v/2), the mean square quantization error is
q2 =1
∆v
ˆ ∆v/2
−∆v/2q2dq =
(∆v)2
12. (6)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization Error
Quantization error is defined as
q (t) = m (t)−m (t). (4)
From the figure shown in the previous slide,
−∆v/2 ≤ q (t) ≤ ∆v/2, (5)
where∆v = 2mp/L.
Assuming that the error is equally likely to lie anywhere in the range(−∆v/2,+∆v/2), the mean square quantization error is
q2 =1
∆v
ˆ ∆v/2
−∆v/2q2dq =
(∆v)2
12. (6)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 106: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/106.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization Error
Quantization error is defined as
q (t) = m (t)−m (t). (4)
From the figure shown in the previous slide,
−∆v/2 ≤ q (t) ≤ ∆v/2, (5)
where∆v = 2mp/L.
Assuming that the error is equally likely to lie anywhere in the range(−∆v/2,+∆v/2), the mean square quantization error is
q2 =1
∆v
ˆ ∆v/2
−∆v/2q2dq =
(∆v)2
12. (6)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Quantization Error
Quantization error is defined as
q (t) = m (t)−m (t). (4)
From the figure shown in the previous slide,
−∆v/2 ≤ q (t) ≤ ∆v/2, (5)
where∆v = 2mp/L.
Assuming that the error is equally likely to lie anywhere in the range(−∆v/2,+∆v/2), the mean square quantization error is
q2 =1
∆v
ˆ ∆v/2
−∆v/2q2dq =
(∆v)2
12. (6)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal to Quantization Noise Ratio (SQNR)
Now that we got mean square quantization error, we can obtain SQNR asshown below:
SQNR =So
No=
m2 (t)
q2 (t)=
12m2 (t)
(∆v)2 . (7)
Since ∆v = 2mp/L,
SQNR = 3L2 m2 (t)m2
p. (8)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal to Quantization Noise Ratio (SQNR)
Now that we got mean square quantization error, we can obtain SQNR asshown below:
SQNR =So
No=
m2 (t)
q2 (t)=
12m2 (t)
(∆v)2 . (7)
Since ∆v = 2mp/L,
SQNR = 3L2 m2 (t)m2
p. (8)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Signal to Quantization Noise Ratio (SQNR)
Now that we got mean square quantization error, we can obtain SQNR asshown below:
SQNR =So
No=
m2 (t)
q2 (t)=
12m2 (t)
(∆v)2 . (7)
Since ∆v = 2mp/L,
SQNR = 3L2 m2 (t)m2
p. (8)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Non-Uniform Quantization
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.10.20.30.40.50.60.70.80.91.0
Speech signal magnitudes relativeto the rms of such magnitudes
Prob
ablit
y th
at
absc
issa
val
ue is
exc
eede
d
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Non-Uniform Quantization
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.10.20.30.40.50.60.70.80.91.0
Speech signal magnitudes relativeto the rms of such magnitudes
Prob
ablit
y th
at
absc
issa
val
ue is
exc
eede
d
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Non-Uniform Quantization
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.10.20.30.40.50.60.70.80.91.0
Speech signal magnitudes relativeto the rms of such magnitudes
Prob
ablit
y th
at
absc
issa
val
ue is
exc
eede
d
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Non-Uniform Quantization
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.10.20.30.40.50.60.70.80.91.0
Speech signal magnitudes relativeto the rms of such magnitudes
Prob
ablit
y th
at
absc
issa
val
ue is
exc
eede
d mp
-mp
m(t)
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Non-Uniform Quantization
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.10.20.30.40.50.60.70.80.91.0
Speech signal magnitudes relativeto the rms of such magnitudes
Prob
ablit
y th
at
absc
issa
val
ue is
exc
eede
d mp
Quantizationlevels
-mp
m(t)
t
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Compressor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Compressor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Compressor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Compressor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Expandor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Expandor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Expandor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Expandor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Expandor
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 125: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/125.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Companding
+
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
The Companding
+
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
µ Law
μ = 0
μ = 10μ = 100
μ = 1000
y =1
ln (1 + µ)ln(
1 +µmmp
), 0 ≤ m
mp≤ 1 (9)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
µ Law
μ = 0
μ = 10μ = 100
μ = 1000
y =1
ln (1 + µ)ln(
1 +µmmp
), 0 ≤ m
mp≤ 1 (9)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
µ Law
μ = 0
μ = 10μ = 100
μ = 1000
y =1
ln (1 + µ)ln(
1 +µmmp
), 0 ≤ m
mp≤ 1 (9)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Law
A = 1
A = 10A = 87.6
A = 1000
y =
A
1+ln A
(mmp
)0 ≤ m
mp≤ 1
A1
1+ln A
(1 + ln Am
mp
)1A ≤
mmp≤ 1
(10)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Law
A = 1
A = 10A = 87.6
A = 1000
y =
A
1+ln A
(mmp
)0 ≤ m
mp≤ 1
A1
1+ln A
(1 + ln Am
mp
)1A ≤
mmp≤ 1
(10)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
A Law
A = 1
A = 10A = 87.6
A = 1000
y =
A
1+ln A
(mmp
)0 ≤ m
mp≤ 1
A1
1+ln A
(1 + ln Am
mp
)1A ≤
mmp≤ 1
(10)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
SQNR (µ Law)
0 10 20 30 40 50 60
10
20
30
40
50
0
Relative signal power m2(t), dB
SNR,
dB
L = 256μ = 0
μ = 255
So
No' 3L2
[ln (1 + µ)]2, µ2 �
m2p
m2 (t)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
SQNR (µ Law)
0 10 20 30 40 50 60
10
20
30
40
50
0
Relative signal power m2(t), dB
SNR,
dB
L = 256μ = 0
μ = 255
So
No' 3L2
[ln (1 + µ)]2, µ2 �
m2p
m2 (t)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
SQNR (µ Law)
0 10 20 30 40 50 60
10
20
30
40
50
0
Relative signal power m2(t), dB
SNR,
dB
L = 256μ = 0
μ = 255
So
No' 3L2
[ln (1 + µ)]2, µ2 �
m2p
m2 (t)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
SQNR (A Law)
Search for the SQNR expression for A law case.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
SQNR (A Law)
Search for the SQNR expression for A law case.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM
x(t)
1234567
t000 100 101 100 011 100 110 111 101 011 011 100 100
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM
x(t)
1234567
t000 100 101 100 011 100 110 111 101 011 011 100 100
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Pulse Shaping
t
0 Tb 2Tb
Tb = Ts / n = 1/2nB
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – Transmission Bandwidth
For a binary PCM,L = 2n or n = log2 L. (11)
Since there should be at least 2B pulses per second, total number of bits persecond are 2nB.
So, minimum channel bandwidth is
BT = nB Hz. (12)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – Transmission Bandwidth
For a binary PCM,L = 2n or n = log2 L. (11)
Since there should be at least 2B pulses per second, total number of bits persecond are 2nB.
So, minimum channel bandwidth is
BT = nB Hz. (12)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – Transmission Bandwidth
For a binary PCM,L = 2n or n = log2 L. (11)
Since there should be at least 2B pulses per second, total number of bits persecond are 2nB.
So, minimum channel bandwidth is
BT = nB Hz. (12)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – Transmission Bandwidth
For a binary PCM,L = 2n or n = log2 L. (11)
Since there should be at least 2B pulses per second, total number of bits persecond are 2nB.
So, minimum channel bandwidth is
BT = nB Hz. (12)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
We have already derived the expression
SQNR = 3L2 m2 (t)m2
p.
Since for binary PCM, L = 2n,
SQNR = 3 (2n)2 m2 (t)m2
p= c22n,
where c = 3 m2(t)m2
pfor uncompressed casea.
Since n = BT/B,SNR = c22BT/B. (13)
aFor µ law case, c = 3/ [ln (1 + µ)]2 .
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
We have already derived the expression
SQNR = 3L2 m2 (t)m2
p.
Since for binary PCM, L = 2n,
SQNR = 3 (2n)2 m2 (t)m2
p= c22n,
where c = 3 m2(t)m2
pfor uncompressed casea.
Since n = BT/B,SNR = c22BT/B. (13)
aFor µ law case, c = 3/ [ln (1 + µ)]2 .
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
We have already derived the expression
SQNR = 3L2 m2 (t)m2
p.
Since for binary PCM, L = 2n,
SQNR = 3 (2n)2 m2 (t)m2
p= c22n,
where c = 3 m2(t)m2
pfor uncompressed casea.
Since n = BT/B,SNR = c22BT/B. (13)
aFor µ law case, c = 3/ [ln (1 + µ)]2 .
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
We have already derived the expression
SQNR = 3L2 m2 (t)m2
p.
Since for binary PCM, L = 2n,
SQNR = 3 (2n)2 m2 (t)m2
p= c22n,
where c = 3 m2(t)m2
pfor uncompressed casea.
Since n = BT/B,SNR = c22BT/B. (13)
aFor µ law case, c = 3/ [ln (1 + µ)]2 .
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
SQNR is given asSNR = c22n.
Applying dB scale on both sides of the above equation gives
(SQNR)dB = 10 log10 c + 20n log10 2 = (α + 6n) dB. (14)
An increase in the code word size by 1 bit, the SQNR increases by 6 dB and BTbecomes (n + 1)B.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
SQNR is given asSNR = c22n.
Applying dB scale on both sides of the above equation gives
(SQNR)dB = 10 log10 c + 20n log10 2 = (α + 6n) dB. (14)
An increase in the code word size by 1 bit, the SQNR increases by 6 dB and BTbecomes (n + 1)B.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
SQNR is given asSNR = c22n.
Applying dB scale on both sides of the above equation gives
(SQNR)dB = 10 log10 c + 20n log10 2 = (α + 6n) dB. (14)
An increase in the code word size by 1 bit, the SQNR increases by 6 dB and BTbecomes (n + 1)B.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Binary PCM – SQNR
SQNR is given asSNR = c22n.
Applying dB scale on both sides of the above equation gives
(SQNR)dB = 10 log10 c + 20n log10 2 = (α + 6n) dB. (14)
An increase in the code word size by 1 bit, the SQNR increases by 6 dB and BTbecomes (n + 1)B.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Self Study
• Digital telephony
• T1 carriers
• Digital multiplexing
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Self Study
• Digital telephony
• T1 carriers
• Digital multiplexing
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Self Study
• Digital telephony
• T1 carriers
• Digital multiplexing
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Self Study
• Digital telephony
• T1 carriers
• Digital multiplexing
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 163: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/163.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Outline
1 Sampling Theorem
2 Pulse Code Modulation
3 Differential Pulse Code Modulation
4 Delta Modulation
5 Summary
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
PCM is not efficient as it requires bit-rate Rb = 2nB bits/sec (nB HzTransmission bandwidth).
There exist other methods that result in to less bit rates. They exploit theinherent characteristics of the underlying signal.
These techniques are also considered as compression techniques.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
PCM is not efficient as it requires bit-rate Rb = 2nB bits/sec (nB HzTransmission bandwidth).
There exist other methods that result in to less bit rates. They exploit theinherent characteristics of the underlying signal.
These techniques are also considered as compression techniques.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
PCM is not efficient as it requires bit-rate Rb = 2nB bits/sec (nB HzTransmission bandwidth).
There exist other methods that result in to less bit rates. They exploit theinherent characteristics of the underlying signal.
These techniques are also considered as compression techniques.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
PCM is not efficient as it requires bit-rate Rb = 2nB bits/sec (nB HzTransmission bandwidth).
There exist other methods that result in to less bit rates. They exploit theinherent characteristics of the underlying signal.
These techniques are also considered as compression techniques.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
![Page 168: 6: Digital Representation of Analog Signals · 5 Summary 6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad. Sampling TheoremPulse Code](https://reader034.vdocument.in/reader034/viewer/2022051511/60158efa625dae78e058aafa/html5/thumbnails/168.jpg)
Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
In analog messages, we can make a good guess about the sample value froma knowledge of the past sample values.
Proper exploitation of this redundancy leads to encoding a signal with alesser number of bits.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
In analog messages, we can make a good guess about the sample value froma knowledge of the past sample values.
Proper exploitation of this redundancy leads to encoding a signal with alesser number of bits.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
In analog messages, we can make a good guess about the sample value froma knowledge of the past sample values.
Proper exploitation of this redundancy leads to encoding a signal with alesser number of bits.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
m(t)
t
Instead of transmitting sample values, we can transmit the differencebetween the consecutive sample values.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
m(t)
t
Instead of transmitting sample values, we can transmit the differencebetween the consecutive sample values.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
m[k]
t
m[k]>
Instead of transmitting sample values, we can transmit the differencebetween the consecutive sample values.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
m[k]
t
m[k]>
Instead of transmitting sample values, we can transmit the differencebetween the consecutive sample values.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
Is there any other better estimation technique to reduce the amplitude of thetransmitted difference signal further?
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
Is there any other better estimation technique to reduce the amplitude of thetransmitted difference signal further?
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
t
m[k]m[k]>
We can reduce the amplitude of the difference signal by taking more numberof past samples into consideration.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
t
m[k]m[k]>
We can reduce the amplitude of the difference signal by taking more numberof past samples into consideration.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Why Differential Pulse Code Modulation (DPCM)?
t
m[k]m[k]>
We can reduce the amplitude of the difference signal by taking more numberof past samples into consideration.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
For a given analog signal, using the Taylor series, we can predict (estimate)the future value as shown below:
m (t + ∆t) = m (t) + ∆tm (t) +(∆t)2
2!m (t) +
(∆t)3
3!...m (t) + · · · (15)
≈ m (t) + ∆tm (t) = m (t) (16)
A discrete version of the above equation is
m [k + 1] ≈ m [k] + Ts
[m [k]−m [k− 1]
Ts
]= 2m [k]−m [k− 1]. (17)
The above equation can be rewritten as
m [k] ≈ m [k] = 2m [k− 1]−m [k− 2]. (18)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
For a given analog signal, using the Taylor series, we can predict (estimate)the future value as shown below:
m (t + ∆t) = m (t) + ∆tm (t) +(∆t)2
2!m (t) +
(∆t)3
3!...m (t) + · · · (15)
≈ m (t) + ∆tm (t) = m (t) (16)
A discrete version of the above equation is
m [k + 1] ≈ m [k] + Ts
[m [k]−m [k− 1]
Ts
]= 2m [k]−m [k− 1]. (17)
The above equation can be rewritten as
m [k] ≈ m [k] = 2m [k− 1]−m [k− 2]. (18)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
For a given analog signal, using the Taylor series, we can predict (estimate)the future value as shown below:
m (t + ∆t) = m (t) + ∆tm (t) +(∆t)2
2!m (t) +
(∆t)3
3!...m (t) + · · · (15)
≈ m (t) + ∆tm (t) = m (t) (16)
A discrete version of the above equation is
m [k + 1] ≈ m [k] + Ts
[m [k]−m [k− 1]
Ts
]= 2m [k]−m [k− 1]. (17)
The above equation can be rewritten as
m [k] ≈ m [k] = 2m [k− 1]−m [k− 2]. (18)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
For a given analog signal, using the Taylor series, we can predict (estimate)the future value as shown below:
m (t + ∆t) = m (t) + ∆tm (t) +(∆t)2
2!m (t) +
(∆t)3
3!...m (t) + · · · (15)
≈ m (t) + ∆tm (t) = m (t) (16)
A discrete version of the above equation is
m [k + 1] ≈ m [k] + Ts
[m [k]−m [k− 1]
Ts
]= 2m [k]−m [k− 1]. (17)
The above equation can be rewritten as
m [k] ≈ m [k] = 2m [k− 1]−m [k− 2]. (18)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
The approximation becomes more accurate as we add more number of termsin the series (15). This requires more number of samples in the past.
So, a more general expression for estimation is
m [k] ≈ m [k] = a1m [k− 1] + a2m [k− 2] + · · ·+ aNm [k−N] . (19)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
The approximation becomes more accurate as we add more number of termsin the series (15). This requires more number of samples in the past.
So, a more general expression for estimation is
m [k] ≈ m [k] = a1m [k− 1] + a2m [k− 2] + · · ·+ aNm [k−N] . (19)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Differential Estimation of m (t) and m [k]
The approximation becomes more accurate as we add more number of termsin the series (15). This requires more number of samples in the past.
So, a more general expression for estimation is
m [k] ≈ m [k] = a1m [k− 1] + a2m [k− 2] + · · ·+ aNm [k−N] . (19)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Transversal Filter used as a Line Predictor
DelayTs
Input m[k]
Output m[k]
a1
DelayTs
DelayTs
DelayTs
DelayTs
aNaN-1a2
>
Σ
m [k] ≈ m [k] = a1m [k− 1] + a2m [k− 2] + · · ·+ aNm [k−N]
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Transversal Filter used as a Line Predictor
DelayTs
Input m[k]
Output m[k]
a1
DelayTs
DelayTs
DelayTs
DelayTs
aNaN-1a2
>
Σ
m [k] ≈ m [k] = a1m [k− 1] + a2m [k− 2] + · · ·+ aNm [k−N]
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Transversal Filter used as a Line Predictor
DelayTs
Input m[k]
Output m[k]
a1
DelayTs
DelayTs
DelayTs
DelayTs
aNaN-1a2
>
Σ
m [k] ≈ m [k] = a1m [k− 1] + a2m [k− 2] + · · ·+ aNm [k−N]
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k]
mq[k]
Σ
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k]
mq[k]
Σ
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k] dq[k]
mq[k]
QuantizerTo channelΣ
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k] dq[k]
mq[k]
mq[k]
QuantizerTo channel
++
Σ
Σ
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k] dq[k]
mq[k]
mq[k]
Quantizer
Predictor
To channel
++
Σ
Σ
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k] dq[k]
mq[k]
mq[k]
Quantizer
Predictor
To channel
++
Σ
Σ
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k] dq[k]
mq[k]
mq[k]
Quantizer
Predictor
To channel
++
Σ
Σ
>
Input Output
dq[k] mq[k]Σ
mq[k]>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM Transmitter and Receiver
m[k] d[k] dq[k]
mq[k]
mq[k]
Quantizer
Predictor
To channel
++
Σ
Σ
>
Predictor
Input Output
dq[k] mq[k]Σ
mq[k]>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM – SQNR
Compared to PCM, in DPCM, the quantization step size is reduced for agiven number of levels L which in turn reduces the quantization noise.
For the same number of bits/sample, the SQNR improves (over PCM) byabout 5.6 dB for a 2 step predictor.
For the same SQNR , we require 3-4 bits/ sample less than PCM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM – SQNR
Compared to PCM, in DPCM, the quantization step size is reduced for agiven number of levels L which in turn reduces the quantization noise.
For the same number of bits/sample, the SQNR improves (over PCM) byabout 5.6 dB for a 2 step predictor.
For the same SQNR , we require 3-4 bits/ sample less than PCM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM – SQNR
Compared to PCM, in DPCM, the quantization step size is reduced for agiven number of levels L which in turn reduces the quantization noise.
For the same number of bits/sample, the SQNR improves (over PCM) byabout 5.6 dB for a 2 step predictor.
For the same SQNR , we require 3-4 bits/ sample less than PCM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM – SQNR
Compared to PCM, in DPCM, the quantization step size is reduced for agiven number of levels L which in turn reduces the quantization noise.
For the same number of bits/sample, the SQNR improves (over PCM) byabout 5.6 dB for a 2 step predictor.
For the same SQNR , we require 3-4 bits/ sample less than PCM
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Adaptive DPCM (ADPCM)
In DPCM, the quantization step is fixed. However, the prediction error couldbe small or large, depending on the signal and the predictor accuracy.
So, in ADPCM, the quantization step is made adaptive, depending on theprediction error. Thus, compared to DPCM, ADPCM can further compress
the bit rates.
International Telecommunication Union, (ITU) specifies the standards andadapted ADPCM under G-726 Standard. G.726, for a 8 kHz sampled voice,
has bit rates as: 16, 24, 32 and 40 kbps.
This implies, 2, 3, 4 and 5 bits / sample. Standard PCM has 8 bits/ sample.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Adaptive DPCM (ADPCM)
In DPCM, the quantization step is fixed. However, the prediction error couldbe small or large, depending on the signal and the predictor accuracy.
So, in ADPCM, the quantization step is made adaptive, depending on theprediction error. Thus, compared to DPCM, ADPCM can further compress
the bit rates.
International Telecommunication Union, (ITU) specifies the standards andadapted ADPCM under G-726 Standard. G.726, for a 8 kHz sampled voice,
has bit rates as: 16, 24, 32 and 40 kbps.
This implies, 2, 3, 4 and 5 bits / sample. Standard PCM has 8 bits/ sample.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Adaptive DPCM (ADPCM)
In DPCM, the quantization step is fixed. However, the prediction error couldbe small or large, depending on the signal and the predictor accuracy.
So, in ADPCM, the quantization step is made adaptive, depending on theprediction error. Thus, compared to DPCM, ADPCM can further compress
the bit rates.
International Telecommunication Union, (ITU) specifies the standards andadapted ADPCM under G-726 Standard. G.726, for a 8 kHz sampled voice,
has bit rates as: 16, 24, 32 and 40 kbps.
This implies, 2, 3, 4 and 5 bits / sample. Standard PCM has 8 bits/ sample.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Adaptive DPCM (ADPCM)
In DPCM, the quantization step is fixed. However, the prediction error couldbe small or large, depending on the signal and the predictor accuracy.
So, in ADPCM, the quantization step is made adaptive, depending on theprediction error. Thus, compared to DPCM, ADPCM can further compress
the bit rates.
International Telecommunication Union, (ITU) specifies the standards andadapted ADPCM under G-726 Standard. G.726, for a 8 kHz sampled voice,
has bit rates as: 16, 24, 32 and 40 kbps.
This implies, 2, 3, 4 and 5 bits / sample. Standard PCM has 8 bits/ sample.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Adaptive DPCM (ADPCM)
In DPCM, the quantization step is fixed. However, the prediction error couldbe small or large, depending on the signal and the predictor accuracy.
So, in ADPCM, the quantization step is made adaptive, depending on theprediction error. Thus, compared to DPCM, ADPCM can further compress
the bit rates.
International Telecommunication Union, (ITU) specifies the standards andadapted ADPCM under G-726 Standard. G.726, for a 8 kHz sampled voice,
has bit rates as: 16, 24, 32 and 40 kbps.
This implies, 2, 3, 4 and 5 bits / sample. Standard PCM has 8 bits/ sample.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Outline
1 Sampling Theorem
2 Pulse Code Modulation
3 Differential Pulse Code Modulation
4 Delta Modulation
5 Summary
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m[k] d[k] dq[k]
mq[k]
mq[k]
Quantizer
Predictor
To channel
++
Σ
Σ
>
Predictor
Input Output
dq[k] mq[k]Σ
mq[k]>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m[k] d[k] dq[k]
mq[k]
mq[k]
Quantizer
Predictor
To channel
++
Σ
Σ
>
Predictor
Input Output
dq[k] mq[k]Σ
mq[k]>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m[k] d[k] dq[k]
mq[k-1]
mq[k]
1-bitQuantizer
Delay Ts
To channel
++
Σ
Σ Input Output
dq[k] mq[k]Σ
mq[k-1]
Delay Ts
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM vs DM
Since we are using only first order predictor (delay Ts), there should be anincreased correlation between adjacent samples.
This can be achieved by oversampling (typically 4 times Nyquist rate) of thebaseband signal.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM vs DM
Since we are using only first order predictor (delay Ts), there should be anincreased correlation between adjacent samples.
This can be achieved by oversampling (typically 4 times Nyquist rate) of thebaseband signal.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
DPCM vs DM
Since we are using only first order predictor (delay Ts), there should be anincreased correlation between adjacent samples.
This can be achieved by oversampling (typically 4 times Nyquist rate) of thebaseband signal.
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
Error d(t)
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation (DM)
Error d(t)
dq[k]
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation and Demodulation
m(t) d(t)Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation and Demodulation
m(t) d(t)Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation and Demodulation
Comparator
m(t) E
-E
dq(t)d(t)Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation and Demodulation
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation and Demodulation
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Delta Modulation and Demodulation
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
mq(t)
>
LPF
Amplifier-Integrator
dq[k] m(t)~
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Threshold and Overloading
StartupSlope
overload
m(t)mq(t)
>
Threshold effect
Slope overload noise can be decresed by increasing the step size. However,this increases the granular noise (which is similar to quantization noise).
No overload occurs if|m (t)| < σfs. (20)
So, for tone modulation (i. e., when m (t) = A cos ωt)
|m (t)| = ωA < σfs. (21)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Threshold and Overloading
StartupSlope
overload
m(t)mq(t)
>
Threshold effect
Slope overload noise can be decresed by increasing the step size. However,this increases the granular noise (which is similar to quantization noise).
No overload occurs if|m (t)| < σfs. (20)
So, for tone modulation (i. e., when m (t) = A cos ωt)
|m (t)| = ωA < σfs. (21)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Threshold and Overloading
StartupSlope
overload
m(t)mq(t)
>
Threshold effect
Slope overload noise can be decresed by increasing the step size. However,this increases the granular noise (which is similar to quantization noise).
No overload occurs if|m (t)| < σfs. (20)
So, for tone modulation (i. e., when m (t) = A cos ωt)
|m (t)| = ωA < σfs. (21)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Threshold and Overloading
StartupSlope
overload
m(t)mq(t)
>
Threshold effect
Slope overload noise can be decresed by increasing the step size. However,this increases the granular noise (which is similar to quantization noise).
No overload occurs if|m (t)| < σfs. (20)
So, for tone modulation (i. e., when m (t) = A cos ωt)
|m (t)| = ωA < σfs. (21)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Threshold and Overloading
StartupSlope
overload
m(t)mq(t)
>
Threshold effect
Slope overload noise can be decresed by increasing the step size. However,this increases the granular noise (which is similar to quantization noise).
No overload occurs if|m (t)| < σfs. (20)
So, for tone modulation (i. e., when m (t) = A cos ωt)
|m (t)| = ωA < σfs. (21)
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (Double Integration)
Frequency, Hz
Relative amplitude, dB
100 200 500 1000 5000 10000
010203040
5060
Single integrationin the
feedback loop
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (Double Integration)
Frequency, Hz
Relative amplitude, dB
100 200 500 1000 5000 10000
010203040
5060
Single integrationin the
feedback loop
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (Double Integration)
Frequency, Hz
Relative amplitude, dB
100 200 500 1000 5000 10000
010203040
5060
Single integrationin the
feedback loop
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (Double Integration)
Frequency, Hz
Relative amplitude, dB
100 200 500 1000 5000 10000
010203040
5060
Single integrationin the
feedback loop
Double integrationin the
feedback loop
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (Double Integration)
Frequency, Hz
Relative amplitude, dB
100 200 500 1000 5000 10000
010203040
5060
Single integrationin the
feedback loop
Voicespectrum
Double integrationin the
feedback loop
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (ADM)
dq[k]
Slopeoverload
m(t)mq(t)
>
Threshold effect
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (ADM)
dq[k]
Slopeoverload
m(t)mq(t)
>Threshold effect
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Mitigating Slope Overload Effect (ADM)
dq[k]
m(t)mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Σ− ∆ Modulator
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Σ− ∆ Modulator
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Σ− ∆ Modulator
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
mq(t)
>
LPF
Amplifier-Integrator
dq[k] m(t)~
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Σ− ∆ Modulator
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
mq(t)
>
LPF
Amplifier-Integrator
dq[k] m(t)~
Integrator amplifier
Comparator
Samplerfrequency fs
m(t) E
-E
Integrator amplifier
Σ
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Σ− ∆ Modulator
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
mq(t)
>
LPF
Amplifier-Integrator
dq[k] m(t)~
Integrator amplifier
Comparator
Samplerfrequency fs
m(t) E
-E
Integrator amplifier
Σ LPFm(t)~
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Σ− ∆ Modulator
Comparator
Samplerfrequency fs
m(t) E
-E
dq(t)d(t)
Integrator amplifier
Σ
mq(t)
>
mq(t)
>
LPF
Amplifier-Integrator
dq[k] m(t)~
Integrator amplifier
Comparator
Samplerfrequency fs
m(t) E
-ELPF
m(t)~
Σ
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Outline
1 Sampling Theorem
2 Pulse Code Modulation
3 Differential Pulse Code Modulation
4 Delta Modulation
5 Summary
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad
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Sampling Theorem Pulse Code Modulation Differential Pulse Code Modulation Delta Modulation Summary
Summary
• ∆v = 2mp/L, where L = 2n
• q2 = (∆v)2
12
• SQNRuniform = m2
q2=
12m2(t)(∆v)2 = 3L2 m2(t)
m2p
(uniform quantization)
• SQNRµ ' 3L2
[ln(1+µ)]2, µ2 � m2
p
m2(t)
• Minimum transmission bandwidth required for PCM is Rb2
6: Digital Representation of Analog Signals Communication Systems, Dept. of EEE, BITS Hyderabad