MATLAB Code for Sampling Theorem and effect of under sampling
%Sampling and recovery of signal
df=0.1;
T=10*10^(-3); %Sampling Period
Ts=1/10000;
fs=1/Ts;
t=0:Ts:10;
N=size(t);
s=zeros(N);
s(1:50)=ones(size(s(1:50)));
figure(1);
subplot(2,2,1);
plot(t,s);
xlabel(‘Time’);
ylabel(‘Amplitude’);
title(‘Rectangle Pulse ‘);
axis([0 0.015 0 1.2]);
Y=fft(s);
P2 = abs(Y/fs);%Two Sided Spectrum
subplot(2,2,2);
f1=fftshift(P2);
f=-length(f1)/2:1:length(f1–1)/2–1;
plot(f,f1);
ylabel(‘Amplitude ‘);
title(‘Fourier Spectrum of Rect. Pulse ‘);
grid on
msg=sin(2*pi*5*t)+sin(2*pi*15*t);
subplot(2,2,3);
plot(t,msg);
xlabel(‘Time’);
ylabel(‘Amplitude’);
title(‘Message Pulse ‘);
axis([0 0.11 -0.2 2]);
Y=fft(msg);
P2 = abs(Y/fs);%Two Sided Spectrum
subplot(2,2,4);
f1=fftshift(P2);
f=-length(f1)/2:1:length(f1–1)/2–1;
plot(f,f1);
ylabel(‘Amplitude ‘);
axis([-200 200 -0.2 6]);
title(‘Fourier Spectrum of Msg. Signal ‘);
grid on
figure(2);
pul=square(2*pi*300*t)/2 + 0.5;
subplot(2,2,1);
plot(t,pul);
title(‘Sampling Pulse ‘);
axis([0 0.15 -0.1 1.2]);
smp=pul.*msg;
subplot(2,2,2);
plot(t,smp);
title(‘Sampled Signal ‘);
axis([0 0.1 -0.2 2]);
Y=fft(smp);
P2 = abs(Y/fs);%Two Sided Spectrum
subplot(2,2,3);
f1=fftshift(P2);
f=-length(f1)/2:1:length(f1–1)/2–1;
plot(f,f1);
ylabel(‘Amplitude ‘);
title(‘Fourier Spectrum of Sampled Signal ‘);
grid on
lp=smp;
lp=lowpass(smp,30,50);
subplot(2,2,4);
plot(t,lp);
grid on;
xlabel(‘Time’);
ylabel(‘Amplitude’);
title(‘Low pass filter output ‘);
axis([0 0.1 -0.2 2]);
N=length(smp);
for i=1:N-1
if smp(i)<=0
smp(i)=0;
end
end
n=1;
a(1)=smp(1);
for i=15:60:N-1;
n=n+1;
a(n)=max(lp(i-14:i+15));
end
figure(3);
subplot(2,2,1);
plot(t(1:length(a)),a);
xlabel(‘Time’);
ylabel(‘Amplitude’);
title(‘Recovered Signal ‘);
axis([0 0.1 -0.2 2]);
Y=fft(a);
P2 = abs(Y/fs);%Two Sided Spectrum
subplot(2,2,2);
f1=fftshift(P2);
f=-length(f1)/2:1:length(f1–1)/2–1;
plot(f,f1);
ylabel(‘Amplitude ‘);
axis([-200 200 -0.2 6]);
title(‘Fourier Spectrum of Rcovered Signal ‘);
Thank me later.
