Principles of Communication system

1

Mrs. Bhavya S, Dr. Rashmi Samanth

Senior Assistant Professor, ECE,

MITE-Moodbidri.

MODULE-5

MITE-Moodabidri

Principles of Communication system

2

MITE-Moodabidri

MODULE-5

​

OUTLINE

​

Sampling and Quantization: Introduction, Why Digitize Analog Sources?, The Sampling process, Pulse Amplitude Modulation, Time Division Multiplexing, Pulse-Position Modulation, Generation of PPM Waves, Detection of PPM Waves.

The Quantization Process, Quantization Noise, Pulse–Code Modulation: Sampling, Quantization, Encoding, Regeneration, Decoding, Filtering, Multiplexing, Application to Vocoder

Pulse amplitude modulation(PAM):

MITE

The amplitude of a carrier consisting of periodic train of rectangular pulses is varied in proportion to sample values of a message signal.

Pulse amplitude modulation(PAM):

MITE

• Pulse duration constant.
• It is same as the flat-top

sampling .

• PAM requires wide band of frequencies to transmitt.
• Let v(t) be the carrier signal(rectangular train of pulse)then PAM wave is

Pulse amplitude modulation(PAM):

MITE

Analog Signal

Amplitude Modulated Pulses

Time-Division Multiplexing(TDM):

MITE

TDM is a technique used for transmitting several message signals over a single communication channel by dividing the time frame into slots, one slot for each message signal.

TDM Transmitter:

MITE

TDM receiver:

MITE

Ts =1/fs

Thus time interval Ts contains one sample from each input. This is called frame.

Let there be ‘N’ input channels. Then in each frame there will be one sample from each on the ‘N’ channels. Therefore pulse to pulse spacing between two samples in the frame will be equal to Ts/ N.

Number of pulse per second = 1/spacing b.w two pulses

= N/Ts

=N fs Transmission B.W of TDM channel will be BT = ½ Nfs fs= nyquist rate , then BT = (½ N )2W = NW

MITE

TDM

The time space between successive samples from any one input will be

Pulse-Position Modulation

10

In PPM, the position of a pulse relative to its unmodulated time of

occurrence is varied in accordance with the message signal

MITE-Moodabidri

Pulse-Position Modulation

11

MITE-Moodabidri

MITE

PCM

PCM

MITE

• PCM consists of three steps to digitize an analog signal:
1. Sampling
2. Quantization
3. Binary encoding
• Before we sample, we have to filter the signal to limit the maximum frequency of the signal as it affects the sampling rate.
• Filtering should ensure that we do not distort the signal, ie remove high frequency components that affect the signal shape.

PCM-Sampling

MITE

• Analog signal is sampled every T_S secs.
• T_s is referred to as the sampling interval.
• f_s = 1/T_s is called the sampling rate or sampling frequency.
• There are 3 sampling methods:
• Ideal - an impulse at each sampling instant
• Natural - a pulse of short width with varying amplitude
• Flattop - sample and hold, like natural but with single amplitude value
• The process is referred to as pulse amplitude modulation PAM and the

outcome is a signal with analog (non integer) values

PCM-Quantization

MITE

• Sampling results in a series of pulses of varying amplitude values ranging between two limits: a min and a max.
• The amplitude values are infinite between the two limits.
• We need to map the infinite amplitude values onto a finite set of known values.
• This is achieved by dividing the distance between min and max into L zones, each of height Δ.

Δ = (max - min)/L

PCM-Quantization Levels

MITE

• The midpoint of each zone is assigned a value from 0 to L-1 (resulting

in L values)

• Each sample falling in a zone is then approximated to the value of the midpoint.

PCM-Quantization

MITE

Figure Input-Output Characteristics of a Mid-Rise type Quantizer

PCM-Quantization

MITE

Figure Input-Output Characteristics of a Mid-Tread type Quantizer

PCM-Quantization Error

MITE

• When a signal is quantized, we introduce an error - the coded

signal is an approximation of the actual amplitude value.

• The difference between actual and coded value (midpoint) is referred to as the quantization error.

​

• The more zones, the smaller Δ which results in smaller errors.
• BUT, the more zones the more bits required to encode the samples -> higher bit rate

PCM-Quantization Noise

MITE

MITE

PCM-Q

Thus for (n+1) bits the SNR is given by

PCM-Quantization Noise

MITE

PCM-Encoding

MITE

Figure Quantization and encoding of a sampled signal

PCM-Line codes

MITE

PCM-Differential Encoding

MITE

PCM-Regeneration

MITE

PCM-Decoder

MITE

• To recover an analog signal from a digitized signal we follow the following steps:
• We use a hold circuit that holds the amplitude value of a pulse till the

next pulse arrives.

• We pass this signal through a low pass filter with a cutoff frequency that is equal to the highest frequency in the pre-sampled signal.
• The higher the value of L, the less distorted a signal is recovered

PCM-Filtering

MITE

• To recover message signal by passing through LPF

• In PCM applications Multiplex different message signals

PCM-Multiplexing

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

And Hold

n

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

n

Pulse Code Modulation (PCM)

Assign Closest Level

3

​

​

2

​

​

1

​

​

0

n

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

n

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

n

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

n

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

n

Each quantization level corresponds to a unique combination of bits. The analog signal is transmitted/ stored as a stream of bits and reconstructed when required.

3

​

​

2

​

​

1

​

​

0

n

Each quantization level corresponds to a unique combination of bits. The analog signal is transmitted/ stored as a stream of bits and reconstructed when required.

3

​

​

2

​

​

1

​

​

0

n

0 0

0 1

1 0

1 1

1 0

0 1

0 0

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

t

x(t)

Original Signal

Pulse Code Modulation (PCM)

3

​

​

2

​

​

1

​

​

0

It is quite apparent that the quantized signal is not exactly the

same as the original analog signal. There is a fair degree of quantization error here. However; as the number of quantization levels is increased the quantization error is reduced and the quantized signal gets closer and closer to the original signal

t

x~(t)

Quantized Signal

Pulse Code Modulation (PCM)

0

It is quite apparent that the quantized signal is not exactly the

same as the original analog signal. There is a fair degree of quantization error here. However; as the number of quantization levels is increased the quantization error is reduced and the quantized signal gets closer and closer to the original signal

t

x~(t)

Quantized Signal

ROBUST QUANTIZATION

MITE

Fig: MODEL OF NON UNIFORM QUANTIZER

ROBUST QUANTIZATION

MITE

• Advantages of Non – Uniform Quantization :
• Higher average signal to quantization noise power ratio than the uniform quantizer when the signal pdf is non uniform which is the case in many practical situation.
• RMS value of the quantizer noise power of a non – uniform quantizer is substantially proportional to the sampled value and hence the effect of the quantizer noise is reduced.

Compression Laws.

MITE

• Two Commonly used logarithmic compression laws are called μ - law and A – law.
• μ – law

Compression Laws.

MITE

• A – law.

Vocoders.

MITE

Vocoders.

MITE

Speech model used in Vocoder

Vocoders. –Channel Vocoder

MITE

Channel Vocoder

References

1. Communication Systems”, Simon Haykins & Moher, 5th Edition, John Willey, India Pvt. Ltd, 2010 .

​

• Modern Digital and Analog Communication Systems, B. P. Lathi, Oxford University Press., 4th edition.

​

• An Introduction to Analog and Digital Communication, Simon Haykins,

John Wiley India Pvt. Ltd., 2008, ISBN 978–81–265–3653–5.

MITE-Moodabidri

48