Pulse Code Modulation (PCM), Theory and Matlab code
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Pulse Code Modulation (PCM), Theory and Matlab code

Pulse Code Modulation (PCM) is a method of digitally representing an analog signal. In PCM, the analog signal is sampled at regular intervals, and the amplitude of the signal at each sample point is quantized to a digital value. The resulting digital values are then encoded and transmitted.

PCM

PCM implementation typically involves the following steps:

  1. Sampling: The analog signal is sampled at regular intervals, typically at a rate of 8,000 to 44,100 samples per second.
  2. Quantization: The amplitude of each sample is quantized to a digital value, typically using 8 to 16 bits per sample.
  3. Encoding: The quantized digital values are encoded into a digital format, such as pulse code modulation (PCM) or pulse density modulation (PDM).
  4. Transmission: The encoded digital signal is transmitted over a communication channel, such as a wired or wireless link.
  5. Decoding: The received digital signal is decoded into quantized digital values.
  6. Reconstruction: The quantized digital values are used to reconstruct the original analog signal by playing back the samples in the correct order and at the correct sampling rate.

It’s worth noting that PCM is the most common method for digitizing analog audio signals, also it is widely used in other fields such as telecommunications and video. However, PCM has some limitations, such as the need for a high sampling rate and a large number of bits per sample to accurately represent the original signal.

Matlab Code

P=5;
t = [0:0.1:1*pi];
sig = 4*sin(t);
Vh=max(sig);
V1=min(sig);
N=3;M=2^N;
S=(Vh-V1)/M;
partition = [V1+S:S:Vh-S];
codebook = [V1+S/2:S:Vh-S/2];
[index,quantized_sig,distor] = quantiz(sig,partition,codebook);

codedsig=de2bi(index,'left-msb');
codedsig=codedsig;
txbits=codedsig(:);
errvec=randsrc(length(txbits),1,[0 1;(1-P/100) P/100]);

rxbits=rem(txbits+errvec,2);
rxbits=reshape(rxbits,N,length(sig));
rxbits=rxbits';
index1=bi2de(rxbits,'left-msb');
reconstructedsig=codebook(index1+1);

figure,
subplot(2,2,1);
stem(t,sig);
xlabel('Time');
title('original signal');

subplot(2,2,2);
stem(t,quantized_sig);
xlabel('time)');
title('quantized signal');
tt=[0:N*length(t)-1];

subplot(2,2,3);
stairs(tt,txbits);
xlabel('time');
title('PCM Waveform');

subplot(2,2,4);
stem(t,reconstructedsig);
xlabel('time');
title('received signal');

Output

PCM OUTPUT

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