pulsecode modulation using matlab/PCM using Matlab

Pulse code Modulation:

                By observing the name we think this is a modulation process but in reality this a one type of A to D conversion mechanism i.e. analog to digital conversion technique. Beside this technique we have lot of methods like delta modulation, differential pulse code modulation, adaptive delta modulation, adaptive differential pulse code modulation etc in digital communications. There is always a trade of between all these methods we compare all these based on the bit rate, circuit implementation, and bandwidth. PCM uses lot of operations to convert analog signal to digital signal so the technique is complex.  At the receiver side we employ sampling, quantizing, encoding. Generally the two process named as encoding and quantizing are done in the same circuit known as analog to digital converter i.e. A to D converter. The operations done in the receiver circuit are regeneration of the received signal, decoder, and reconstruction or regeneration. All these operations are performed on the quantized samples. All these operations are done in the same circuit which is digital to analog converter i.e. D to A converter. We know that in the process of transmission we face lot of problems with atmospheric noise and distortion and filtering action of the channel. To combat all these effects we employ regenerating repeaters in the channel to reconstruct and re transmit the coded pulses which are in the way to the receiver. This is time to deal all the processes used in the PCM.  A PCM stream is a digital representation of an analog signal, in which the magnitude of the analog signal is sampled regularly at uniform intervals, with each sample being quantized to the nearest value within a range of digital steps. . This is the standard form used for digital audio in computers, CD and DVD formats. PCM has two properties namely sampling rate and bit depth we all know about sampling rate bit depth refers to the number of digital values that the each sample can take. Quantization error is the main drawback of PCM.

Sampling:

Digital communications requires sampling which is first step in all A to D converters. The sampling is done according to the Nyquist criterion. We may define the process of sampling as a band-limited signal of finite energy, which has no frequency components higher than W hertz, may be completely recovered from the knowledge of its samples taken at the rate of 2W per second. The other definition is a band-limited signal of finite energy, which has no frequency components higher than W hertz, is completely described by specifying the values of the signal at instants of time separated by  seconds. We use these to definitions at the receiver and transmitter. The sampling rate 2W is called the Nyquist rate. And its inverse is called the Nyquist interval. To make the signal as the band limited signal we incorporate the low pass filter at the beginning of the transmitter known as the anti-aliasing filter which stops or attenuates the high frequency components which lie outside the desired frequency band. Then the filtered signal is sampled at a rate higher than the Nyquist rate. A circuit known as the sample and hold circuit is used in sampling to produce the flat top sampling. Flat top sampling provides us to use simple quantizing strategy. Over sampling is used to reduce the distortion in most of the analog to digital converters.

Quantizing:

                Quantization in DSP represents the process which maps the large set values to a single value. A circuit which performs this operation is called the quantizer. This process is also introduces some errors in the signal this is called quantization error or rounding of error. This is a non linear process because this is many to one mapping function. Quantized sample has discrete nature in both time and amplitude. Quantizers are of two types namely uniform and non uniform. In uniform quantization step size is constant while in non uniform quantization step size is varied according to the amplitude of the signal. To perform non uniform quantization one needs to pass the signal into the compressor and then into the uniform quantizer. Non uniform quantization takes care of both high and small variations in the amplitude levels of the signal. we have two laws to perform the quantization they are A-law and µ-law. In the receiver we perform the inverse operation of the quantizer in this we send the received signal into the expander. The device which can perform both operations of expansion and compression is called compander.

Encoding:

                Encoding is done to transmit the signal obtained by the combined effect of the sampling and quantizing over the channel which has undesired characteristics. The signal obtained from the sampling and quantizing is not suitable for transmission as it is over a telephone line i.e. copper pair or radio or microwave link. To combat with the channel impairments we use encoding process. For this we use different types of coding techniques. Encoding process is a one to one representation. A particular arrangement of symbols used in a code to represent a single value of the discrete set is called a code word or character. In a binary code each symbol may be represented by the any two levels of presence of pulse or absence of pulse. Binary wave is robust to noise and easy to regenerate. For example in a binary code each sample is represented with the n number of bits then we can represent the total of 2ⁿ discrete levels.

Program:

clear all
close all
clc
t=[0:0.01:3]             %  time
x=sinc(2*pi*t)              %  mesaage signal

%%%%    compressing the signal using mu law one way of quantizing     %%%%

c=compand(x,255,1,'mu/compressor')      %%% the value for mu used here is 255 here 1 represents the maximim value of messagesignal

%%%%    encoding the signal after quantizing   %%%%%

e=uencode(c,3)

%%%%    decodong the signal after receiving   %%%%%

d=udecode(e,3)   %the quantizing levels are 3 if levels are increased the origional and received signal are highly correlate try for 8 instead of 3

%%%%    expanding the received signal    %%%%%

o=compand(d,255,1,'mu/expander')

%%%%%%%     plotting the graphs     %%%%%

figure(1)
hold on                  %for plotting figures on same window for comparision purpose
plot(x,'--red')
plot(o,'black')
hleg=legend('origional signal','received signal using companding')
hold off

%%%%%%%     pcm with out companding     %%%%%%%%

e1=uencode(x,3)
d1=udecode(e1,3)

%%%%%%%%%%%%%%%%%           plotting figures      %%%%%%%%%%%%

figure(2)                   %%% in this case same step size is constant so tracking the origional signal exatly failed
hold on
plot(x,'-.red')
plot(d1,'green')
hleg=legend('origional signal','received signal without companding')
hold off