07 lecture
TRANSCRIPT
Introduction to Telecommunication
M J Khan
Lecture 07
Menu
• Frequency and frequency domain
• Fourier Transform
• Discrete Fourier Transform (DFT)
• Signal Encoding Techniques
• Bit Encoding Techniques
Frequency
• Frequency is the rate of change with respect
to time.
• Change in a short span of time means high
frequency.
• Change over a long span of time means low
frequency.
Time domain VS Frequency domain
Time domain VS Frequency domain
A complete sine wave in the time domain
can be represented by one single spike in
the frequency domain.
Time domain VS Frequency domain
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
Time domain VS Frequency domain
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
Time domain VS Frequency domain
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
Fourier Analysis
Fourier analysis is a tool that changes a time
domain signal to a frequency domain signal
and vice versa.
Fourier Series
Every composite periodic signal can be
represented with a series of sine and cosine
functions. The functions are integral
harmonics of the fundamental frequency “f”
of the composite signal. Using the series we
can decompose any periodic signal into its
harmonics.
Fourier Transform
Fourier Transform gives the frequency
domain of a non-periodic time domain signal.
Discrete Fourier Transform (DFT)
We are living digital age where every signal
is
• Sampled
• Of finite extent
The DFT is the sampled Fourier Transform.
1
0
/2)()(N
t
NstjetfsF
Inverse DFT
In similar fashion we can transform
frequency domain to time domain
1
0
/2)(1
)(N
s
NstjesFN
tf
Example
Let
]123543[)(tf
1
0
/2)()(N
t
NstjetfsF
We know
By Applying we get
]5.1962i 1.0000-0205.1962i - 1.0000-18[)(sF
Frequency Analysis
For more visit the web link
http://www.fourier-series.com/fourierseries2/DFT_tutorial.html
Signal Encoding Techniques
• Digital Data Analog Signal
• Analog Data Analog Signal
• Analog Data Digital Signal
Digital Data Analog Signal
Digital Data Analog Signals
Digital Data Analog Signals
Amplitude Shift Keying
Frequency Shift Keying
Phase Shift Keying
Phase Shift Keying
4-PSK
8-PSK
Quadrature amplitude modulation is a
combination of ASK and PSK so that a
maximum contrast between each signal
unit (bit, dibit, tribit, and so on) is
achieved.
Note:
The 4-QAM and 8-QAM collections
Time domain for an 8-QAM signal
16-QAM collections
Bit and baud
Bit and baud rate comparisonModulation Units Bits/Baud Baud rate Bit Rate
ASK, FSK, 2-PSK Bit 1 N N
4-PSK, 4-QAM Dibit 2 N 2N
8-PSK, 8-QAM Tribit 3 N 3N
16-QAM Quadbit 4 N 4N
32-QAM Pentabit 5 N 5N
64-QAM Hexabit 6 N 6N
128-QAM Septabit 7 N 7N
256-QAM Octabit 8 N 8N
Analog Data Analog Signals
Amplitude Modulation (AM)
Frequency Modulation (FM)
Phase Modulation (PM)
Analog Data Analog Signal
Analog Data Analog Signal
Amplitude Modulation
Angle Modulation
Analog Data Digital Signal
Pulse Code Modulation
Pulse Code Modulation
PCM involves following steps
1. Sampling
2. Quantization
3. Coding
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Analog Signal
Time (seconds)
L
e
v
e
l
s
Nyquist Sampling Theorem
Nyquist Sampling
Theorem
Fs = Fc/2
Nyquist Sampling
Theorem
Fs = Fc/2
Nyquist Sampling
Theorem
Fs = Fc
Nyquist Sampling
Theorem
Fs = Fc
Nyquist Sampling
Theorem
Fs = 1.5*Fc
Nyquist Sampling
Theorem
Fs = 1.5*Fc
Nyquist Sampling
Theorem
Fs = 2*Fc
Nyquist Sampling
Theorem
Fs = 2*Fc
Nyquist Sampling
Theorem
Fs = 4*Fc
Nyquist Sampling
Theorem
Fs = 4*Fc
Nyquist Sampling
Theorem
Fs = 6*Fc
Nyquist Sampling
Theorem
Fs = 6*Fc
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Sampling
Time (seconds)
L
e
v
e
l
s
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Quantization
Time (seconds)
L
e
v
e
l
s
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
After Sampling
Time (seconds)
L
e
v
e
l
s
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
After Quantization
Time (seconds)
L
e
v
e
l
s
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0011
0100
0111
1000
1001
1010
1011
10111011
1010
1001
10001000
0111
10001000
1000
0110
Coding
Time (seconds)
L
e
v
e
l
s
Delta Modulation
Pulse Code Modulation
Delta Modulation involves following
steps
1. Step up or Step down
2. Coding
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Analog Signal
Time (seconds)
L
e
v
e
l
s
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Follow the Difference
Time (seconds)
L
e
v
e
l
s
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Coding
1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0
Time (seconds)
L
e
v
e
l
s
Bit Encoding
1 0 1 0 1 1 0 01
Unipolar NRZ
NRZ-Inverted
(Differential
Encoding)
Bipolar
Encoding
Differential
Manchester
Encoding
Polar NRZ
Manchester
Encoding