PULSE CODE PULSE CODE MODULATIONMODULATION

4.1

PCM BASIC

•Pulse Code Modulation(PCM) is a technique where the message signal is represented by a sequence of coded pulses.

•In PCM, the binary code varies according to the amplitude of analog signal

•It is digitally encoded pulse modulation with pulses are of •It is digitally encoded pulse modulation with pulses are of fixed length and amplitude

Basic elements of a PCM system

Components of PCM encoder

Components of a PCM decoder

PCM Encoder and Decoder

PCM Encoder (3-step process) :

◦ Sampling: sample the analog Continuous time signal every T sec.

According to Nyquist, the sampling rate must be at least twice the highest frequency in the original signal.

◦ Quantization: convert the sample analog value into discrete values (L levels)

Step size (S) = (Vmax - Vmin) / L Step size (S) = (Vmax - Vmin) / L

◦ Encoding:

Convert the quantized value into an n-bit code word, where

Ln 2log

PCM Decoder : DAC, S/H circuit and Reconstruction filter

Sampling

Sampling (Cont’d)

Aliasing Due to Under Sampling

Reconstruction of Sampled SignalReconstruction of Sampled Signal

Reconstruction of Sampled Signal (Cont’d)

Three different sampling methods

Flat Top sampling Circuit

Quantization

Bandwidth of PCM Signals

Bandwidth depends on: bit rate and pulse shape used to represent the data◦ If n is the number of bits in the PCM word

◦ Sampling frequency

◦ Bandwidth sf

1 1

2 2PCM sB R nf

PCM of Speech Signals

Most of the significant spectral components of speech signals are Most of the significant spectral components of speech signals are contained in the range 300-3400 Hz

Nyquist Rate = 2x3400 = 6.8 kHz

Practical Sampling Rate fs= 8 kHz

Number of quantization levels = 256

Number of Bits/Sample n = 8 (log2256 )

Data Rate = nfs = 8x8000 = 64 kbps

The minimum required bandwidth for transmission of a PCM speech signal BWmin = 64/2 = 32 kHz

• Signal to Quantization Noise Ratio of a uniform quantizer is given by:

• Signal to quantization noise power ratio varies linearly with signal power

• Many signals such as speech have a nonuniform distribution.

The amplitude is more likely to be close to zero than to be at

2

2 )(12

S

tmRSNq

Signal to Quantization Noise Ratio in PCM

The amplitude is more likely to be close to zero than to be at higher levels

• Variable step Size is essential to achieve constant SNqR

Nonuniform Quantization

2 4 6 8

2

4

6

-2Input sampleX

Output sampleXQ

-2-4-6-8

Example: Nonuniform 3 bit quantizer

-4

-6

PCM with Companding

Analog Source

Analog Compressor

Sampler Quantizer Encoder

PCM output

Decoder Hold Circuit

Analog Expander

Reconstruction filter

PCM Input

Reconstructed output

• Non-uniform quantization is achieved by, first passing the input signal • Non-uniform quantization is achieved by, first passing the input signal through a “compressor”. The output of the compressor is then passed through a uniform quantizer.

• The combined effect of the compressor and the uniform quantizer is that of a non-uniform quantizer.

• At the receiver the voice signal is restored to its original form by using an expander.

• This complete process of Compressing and Expanding the signal before and after uniform quantization is called Companding.

))(

1ln()1ln(

1

pm

tmv

1

)(0

pm

tm

μ-Law

Where, The value of ‘µ’ used with 8-bit quantizers for voice signals is 255

Non-uniform Quantization

)(tmA

A-Law

1)

)((

ln1 pm

tm

A

Av

)))(

ln(1(ln1

1

pm

tAm

Av

Apmtm 1

0 )(

11 )(

pmtm

A

Compression laws. (a) m -law. (b) A-law.

Ratio of Signal to Quantization noise in PCM with and without Compression

2

2

)]1[ln(

3

LRSN q

References

1. Modern Digital and Analog Communication Systems, B. P. Lathi and Z. Ding, Oxford University Press

2. Principles of Communication Systems, H. Taub and D. L. Schilling, TMH

3. Digital Communications, S. Haykin, Wiley India

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