To understand the operation theory of pulse coded modulation (PCM) & To understand the theory of PCM demodulation circuit using matlab code

Aim:

1.To understand the operation theory of pulse coded modulation (PCM).

2.To understand the theory of PCM demodulation circuit. 

Program:

clc;

clear all;

close all;

f=600; % Generate sinusoidal wave of frequency of 200/300/400/500/600 Hz

t = 0:1e-4:25/f; % Time period varies from 0 to 5/f,10/f,15/f,20/f,25/f

w = 2*pi*f;

sig1 = sin(w*t);

figure,subplot(321); plot(sig1); xlabel('time'); title('original signal');ylabel('Amplitude');

fs=6500 ; %Generate sampled signal with frequwncy of 2500/3500/4500/5500/6500 Hz

Ts = 1/fs;

t2=(0:Ts:25/f);

sig = sin(w*t2);

subplot(323); stem(t2,sig); xlabel('time'); title('sampled signal');ylabel('Amplitude');

Vh=max(sig);Vl=min(sig);

N=4;M=2^N;S=(Vh-Vl)/M; %design N-bit uniform quantizer with stepsize=S

partition = [Vl+S:S:Vh-S]; % Length M-1, to represent M intervals

codebook = [Vl+S/2:S:Vh-S/2]; % Length M, one entry for each interval

[index,quantized_sig,distor] = quantiz(sig,partition,codebook); % Quantize.

subplot(325); stem(t2,quantized_sig); xlabel('time'); title('quantized signal');

codedsig=de2bi(index,'left-msb');

codedsig=codedsig';

txbits=codedsig(:); %serial transmit

tt=[0:N*length(t2)-1];

subplot(322);stairs(tt,txbits); axis([0 30 -2 3]);xlabel('time'); title('PCM waveform');

rxbits=reshape(txbits,N,length(sig));

rxbits=rxbits';

index1=bi2de(rxbits,'left-msb'); %decode

index2=S*index1+Vl+(S/2);

reconstructedsig=index2; %re-quantize

subplot(324);plot(t2,reconstructedsig); xlabel('time'); title('received signal');

Algorithm:

1. Clear command window

2. Clear all variables in workspace window

3. Close all the files in current folder window

4. Generate the sinusoidal expression with frequency(f) to 200/300/400/500/600 Hz

and time(t) from 0 to 5/f, 10/f, 15/f, 20/f, 25/f in interval of

sec.

5. Generate the expression for samples with time(t) from 0 to 5/f, 10/f, 15/f, 20/f, 25/f

in interval of sampling frequency of 2500/3500/4500/5500/6500 Hz

6. Determine maximum and minimum of sampled signal

7. Determine the N value for N-bit uniform quantizer and also step size

8. Determine the no.of intervals, possibly M-1 (M=2N)

9. Determine the no.of entries in each interval, possibly M

10. Perform the quantization process of the sampled signal, determine the quantization

levels and quantized values

11. Plot the quantized values

12. Convert the quantization levels from decimal to binary and transpose it

13. Determine the time duration for PCM encoded signal possibly from 0 to N*(length

of sampled interval)-1

14. Plot the PCM encoded signal using stairs command

15. Reconstruct the original signal from PCM encoded signal, N, no.of elements in

sampled signal and transpose the vector

16. Convert the reconstructed signal from binary to decimal and plot the reconstructed

signal.

Real Time applications:

Computer Disk, Digital Telephony, Digital Audio Applications