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MATLAB code for Pulse Code Modulation (PCM) and Demodulation


MATLAB Code for Pulse Code Modulation


clc;
close all;
clear all;

fm=input('Enter the message frequency (in Hz): ');
fs=input('Enter the sampling frequency (in Hz): ');
L=input('Enter the number of the quantization levels: ');

n = log2(L);


t=0:1/fs:1; % fs nuber of samples have tobe selected

s=8*sin(2*pi*fm*t);
subplot(3,1,1);
t=0:1/(length(s)-1):1;
plot(t,s);
title('Analog Signal');
ylabel('Amplitude--->');
xlabel('Time--->');
subplot(3,1,2);
stem(t,s);grid on; title('Sampled Sinal'); ylabel('Amplitude--->'); xlabel('Time--->');

% Quantization Process
vmax=8;
vmin=-vmax; %to quantize a signal s into L levels between vmin and vmax
del=(vmax-vmin)/L;
part=vmin:del:vmax; % level are between vmin and vmax with difference of del
code=vmin-(del/2):del:vmax+(del/2); % Contaion Quantized valuses
[ind,q]=quantiz(s,part,code); % Quantization process
% ind contain index number and q contain quantized values
l1=length(ind);
l2=length(q);

for i=1:l1
if(ind(i)~=0) % To make index as binary decimal so started from 0 to N
ind(i)=ind(i)-1;
end
i=i+1;
end
for i=1:l2
if(q(i)==vmin-(del/2)) % To make quantize value inbetween the levels
q(i)=vmin+(del/2);
end
end
subplot(3,1,3);
stem(t,q);grid on; % Display the Quantize values
title('Quantized Signal');
ylabel('Amplitude--->');
xlabel('Time--->');

% Encoding Process
figure
code=de2bi(ind,'left-msb'); % Cnvert the decimal to binary
k=1;
for i=1:l1
for j=1:n
coded(k)=code(i,j); % convert code matrix to a coded row vector
j=j+1;
k=k+1;
end
i=i+1;
end
subplot(2,1,1); grid on;
stairs(coded); % Display the encoded signal
axis([0 100 -2 3]); title('Encoded Signal');
ylabel('Amplitude--->');

% Demodulation Of PCM signal

qunt=reshape(coded,n,length(coded)/n);
index=bi2de(qunt','left-msb'); % Getback the index in decimal form
q=del*index+vmin+(del/2); % getback Quantized values
subplot(2,1,2); grid on;
plot(t,q);
title('demodulated signal without low-pass filter');



% % % Demodulation after applying low-pass filter


figure()
% Low-pass Filter Design
fc = fm; % Cutoff frequency for the low-pass filter
order = 1; % Filter order (first-order Butterworth filter)

% Design the low-pass Butterworth filter
[b, a] = butter(order, fc/(fs/2), 'low');

% Apply the low-pass filter to the signal
filtered_signal = filtfilt(b, a, q);
plot(t,s);
title('demodulated signal after applying low-pass filter') 

Output

Enter the message frequency (in Hz): 1
Enter the sampling frequency (in Hz): 10000
Enter the number of the quantization levels:  8
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