ii.a baseband transmission (definitions & modulation types)

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09/23/03 EC2500MPF/FallFY04 1 II.A Baseband Transmission Pulse Amplitude Modulation (PAM) Natural sampled PAM Instantaneous sampled PAM Time division multiplexing (TDM) Intersymbol interference (ISI) Pulse Width Modulation (PWM) Pulse Position Modulation (PPM) Pulse Code Modulation (PCM) Definition Quantization noise issues Signal-to-Quantization Noise ratio (SNR q ) Nonlinear quantization Pre-emphasis & de-emphasis Application to speech signal type -law & A-law quantization for speech types TDM for digital signals Delta modulation Adaptive Delta modulation Receivers PAM, PPM, PWM receivers Digital Baseband Signal format & power spectrum concepts Potential problems with NRZ transmissions (Definitions & Modulation types)

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Page 1: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 1

II.A Baseband Transmission

Pulse Amplitude Modulation (PAM)Natural sampled PAMInstantaneous sampled PAMTime division multiplexing (TDM)Intersymbol interference (ISI)

Pulse Width Modulation (PWM)Pulse Position Modulation (PPM)Pulse Code Modulation (PCM)

DefinitionQuantization noise issuesSignal-to-Quantization Noise ratio (SNRq)Nonlinear quantizationPre-emphasis & de-emphasisApplication to speech signal type�-law & A-law quantization for speech typesTDM for digital signals

Delta modulationAdaptive Delta modulationReceivers

PAM, PPM, PWM receiversDigital BasebandSignal format & power spectrum conceptsPotential problems with NRZ transmissions

(Definitions & Modulation types)

Page 2: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 2

II. Baseband Transmission

• Goal: Investigate information transmission using low frequencies

1) Pulse Amplitude Modulation (PAM)• Natural-sampled PAM

�s(t)sm(t)

sc(t)

s(t)

t

sc(t)

t

sm(t)

t

Page 3: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 3

S(f)

f– fm fm

S1(f)

f

Sm(f)

f

• Natural Sampled PAM from the frequency side

Page 4: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 4

S(f)

f– fm fm

H(f)

S1(f)

f

f

• Natural Sampled PAM from the frequency side

Page 5: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 5

�s(t)sm(t)

sc(t)

H(f)s1(t)

• Instantaneous-sampled PAM

s(t)

t

sc(t)

t

s1(t)

t

t

sm(t)

Page 6: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 6

H(f)

S1(f)

f

f

Sm(f)

f

• Instantaneous Sampled PAM from the frequency side

S(f)

f– fm fm

Page 7: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 7

�s(t) sm(t)

sc(t)

� �sin ts t

t�

sc(t)

t– � � T

Compute the Fourier transform for sm(t)

• Example

Page 8: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 8

Page 9: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 9

2) Time Division Multiplexing (TDM)

Multiplexing of 2 channels

Multiplexing of 10 channels

Page 10: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 10

Figure 2.14 - Sub- and Super-CommutationFigure 2.14 - Sub- and Super-Commutation

Page 11: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 11

• What is it ?

Interaction between multiplepoles due to transmissionchannel distortions.

3) Intersymbol Interference (ISI)

• Overlap of signals into adjacent time slots

Pulse through LPF

Page 12: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 12

Pulse shaping by the Channel

sin(2 )( ) mf t

s tt�

1/ 2 mf

2fm

Ideal LPF Shaping

Page 13: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 13

•How is ISI evaluated ?

=>Through eye pattern generation.

Page 14: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 14

Page 15: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 15

==> Raised cosine filter

� �� � � �

� �0 0

2 20 0

sin 2 cos 22 1 8 /

f t KTfh t A

f t K f t� �

� �

K represents flat portion width of the frequency transform

Raised Cosine Impulse Response

• How to fix the problem ?

Page 16: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 16

Raised Cosine Frequency Characteristic

Page 17: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 17

s(t) sm(t)

sc(t)

PWM

4) Pulse Width Modulation (PWM)

PWM

Page 18: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 18

• PWM Generator

Page 19: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 19

5) Pulse Position Modulation (PPM)

• PPM can be derived from PWM

PWM to PPM

Page 20: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 20

• Signal format

6) Pulse Code Modulation (PCM)

• From analog to digital

Page 21: II.A Baseband Transmission (Definitions & Modulation types)

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• Quantization noise issues

- Quantization error is a measure of effectivenessof a quantization scheme

- Quantization noise level is directly related to thenumber of quantization levels

- Assume quantization error e(n) to be equally likelyto occur in the range D

pdf of e

p(e)

e

s(t)

t

Page 22: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 22

• e(n) statistics

Page 23: II.A Baseband Transmission (Definitions & Modulation types)

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• SNR level due to quantization noise

� �

� �

22

2 2s

qe

E s nSNR

E e n�

� �� �� �� �� �

Page 24: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 24

• Example

� � � �2cos 500s t t��

1) Compute SNRq when using 8-bit PCM

2) Compute the minimum number of bits needed to get SNRq � 20 dB

Page 25: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 25

• Non-linear quantization

(pre-emphasis and de-emphasis concepts)

� Goal: to improve quality of signal to be quantized

� Example

S(f)

f60 Hz

signal distortion

Page 26: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 26

� Example: speech signal

Before applying Before applying mumu-law-law After applying After applying mumu-law-law

Comments ?

Page 27: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 27

• Mu-Law / A-Law quantization for voice transmission

• Mu-Law (USA-Japan); � = 255

• Mu-Law (Europe-South America); A = 87.56

� � � �� �� �

1sgn

1In s

F s sIn

� � � �� �

� �� �� �

1sgn ; 01

1 1sgn ; 11

A sF s s s

In A A

In A ss s

In A A

� � �

� �

s(n) F(S(n))Companding

Page 28: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 28

Input-output characteristic for �-law companding

Page 29: II.A Baseband Transmission (Definitions & Modulation types)

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�-255 Piecewise linear approximation

Same resolution whichwould be obtained fromlinear quantization

1 bit for polarity (1 for x>=0, 0 for x<0)3 bits for identifying the segment4 bits to identify quantization level within each segment

Approximate the �-255 curve by a piecewise linear curveDivide output region into 8 unequal segments (for positive side)Within each segment, uniformly quantize using 4 bits (i.e., 16 regions)

Page 30: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 30

• TDM for digital signals

Example: TDM in T – 1 system

� designed for short distances (15 to 65 km)

� 1.544 megabits/s pulse signal developed for transmission

� signal developed by 24 channel TDM

� each channel sampled at 8 KHz, with 8-bit �-law companding

� each frame each 24 � 8 bits

192 bits used for information 1 bit used for frame synchronization

� transmission rate is

8000 frames/s � 193 bits/frame =

1.544 Mbits/sec

TDM in T-1

Page 31: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 31

7) Delta Modulation

• Simplified 1-bit PCM

• Quantization issues

slope overload granular noise

Page 32: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 32

• Adaptive delta modulation

– designed to overcome slope overload and granular noise issues

– Song algorithm: compares transmitted bit with previous bit.

If sameIf different

; 1; 1

K KK K

�� � � �

�� � � �

Song Algorithm

Page 33: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 33

8) PAM, PPM & PWM Receivers

• PAM receiver (Instantaneous-Sampled PAM)

• Recall frequency transform for for natural-Sampled PAM

f

S(f)

f

Sm(f)

Page 34: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 34

• Sample-and-Hold for PAM demodulation

LPFPAM s(t)

Page 35: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 35

• PWM & PPM receivers

2-step process

Page 36: II.A Baseband Transmission (Definitions & Modulation types)

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9) Digital Baseband

Unipolar/Bipolar waveforms

• Signal Format

RZ & NRZ waveforms

Page 37: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 37

• Power Spectrum (Ex: Periodic NRZ)

t

s(t)

Tb Rb=1/TbTb=T/2

a) Power Spectrum of s(t) ( periodic case: 0 1 0 1 0 …)

V

-V

Page 38: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 38

Page 39: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 39

Figure 2.27

Page 40: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 40

b) Power Spectrum of random NRZ (Extension to nonperiodic s(t) case)

-Use concept of power spectral density (PSD)

- Assume that �T increases in multiples of the bit length (Tb)=> same contribution is added in each period=> restrict integration over one period only

2/ 2 2

/ 2

22

1( )

sin( )

b

b

T j ft

Tb

bb

b

G f Ve dtT

fTV T

fT

� �� � �

� �

2/ 2 2

/ 2

1( ) lim ( )T j ft

TTG f s t e dt

T�

��

��� ��

� �� � ��� �

Def: The PSD for a non periodic signal s(t) isdefined as:

Page 41: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 41

Def: Nominal signal bandwidth: Signal bandwidth up tothe 1st zero of signal spectral lobe

What is the above signal nominal bandwidth ?

Page 42: II.A Baseband Transmission (Definitions & Modulation types)

09/23/03 EC2500MPF/FallFY04 42

• Potential problems with NRZ transmissions

- No transition between one bit to the next- Potential data inversion problems

- Differential coding option:data is represented as changes in levels rather than bythe actual signal level