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Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled regularly at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps.

MATLAB Program:

a=4;
fm=2;
fs=100*fm;
t=0:1/fs:1;%for sampling
x=a*sin(2*pi*fm*t);%let us take one simple sin signla for Pulse code modulation
subplot(5,1,1);
plot(t,x,'r');
xlabel('time');
ylabel('amplitude');
title('Original message signal');
subplot(5,1,2);
stem(t,x,'r');
xlabel('time');
ylabel('amplitude');
title('Sampled message signal');
enc=[];

for(i=1:length(x))
if (x(i)>0 && x(i)<=1)
e=[1 0 0];
xq(i)=0.5;
elseif (x(i)>1 && x(i)<=2)
e=[1 0 1];
xq(i)=1.5;
elseif (x(i)>2 && x(i)<=3)
e=[1 1 0];
xq(i)=2.5;
elseif (x(i)>3 && x(i)<=4)
e=[1 1 1];
xq(i)=3.5;
elseif (x(i)>-4 && x(i)<=-3)
e=[0 0 0];
xq(i)=-3.5;
elseif (x(i)>-3 && x(i)<=-2)
e=[0 0 1];
xq(i)=-2.5;
elseif (x(i)>-2 && x(i)<=-1)
e=[0 1 0];
xq(i)=-1.5;
else (x(i)>-1 && x(i)<=0)
e=[0 1 1];
xq(i)=-0.5;
end
enc=[enc e];
end
subplot(5,1,3);
plot(t,xq,'b');
title('Quantised signla');

X_Q=[];
for i=1:3:length(enc)-2
if(enc(i)==0 && enc(i+1)==0 && enc(i+2)==0)
x_q=-3.5;
elseif(enc(i)==0 && enc(i+1)==0 && enc(i+2)==1)
x_q=-2.5;
elseif(enc(i)==0 && enc(i+1)==1 && enc(i+2)==0)
x_q=-1.5;
elseif(enc(i)==0 && enc(i+1)==1 && enc(i+2)==1)
x_q=-0.5;
elseif(enc(i)==1 && enc(i+1)==0 && enc(i+2)==0)
x_q=0.5;
elseif(enc(i)==1 && enc(i+1)==0 && enc(i+2)==1)
x_q=1.5;
elseif(enc(i)==1 && enc(i+1)==1 && enc(i+2)==0)
x_q=2.5;
elseif(enc(i)==1 && enc(i+1)==1 && enc(i+2)==1)
x_q=3.5;
end
X_Q=[X_Q x_q];
end
subplot(5,1,4);
plot(t,X_Q);
title('Decoded signal');
[num,den]=butter(6,4*fm/fs);
recon=filter(num,den,X_Q);
subplot(5,1,5);
plot(t,recon);