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

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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

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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

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10

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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

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v

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l

s

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1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

After Sampling

Time (seconds)

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v

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l

s

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

After Quantization

Time (seconds)

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v

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s

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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

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12

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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

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10

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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

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v

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l

s

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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