This document contains code for analyzing and verifying the sampling theorem. It contains three parts: 1) Undersampling and oversampling a cosine signal, 2) Commenting on reconstructing a signal from its samples, and 3) Verifying the Nyquist criterion by reconstructing a multi-frequency signal using different sampling rates and observing the reconstruction quality.

1. clear
clc
% Practical : Exp-4 Title: Sampling Theorem
% Name: Omkar Rane
% Batch: 1 Block : 1
% Roll No: SETB118
% Seat No: S177086
%a). To analyze undersampled and oversampled signals.
%_________________________________________________________________________%
a=1;
t=0:1/2000:0.02;
y=a*cos(2*pi*60*t);
subplot(311);
plot(t,y);
xlabel('t');
ylabel('A');
title('Continous cosine');
%________________________________________________________________________%
a=1;
t240 = 0:1/240:0.02;
n240=0:(length(t240)-1);
ts1=1/240;
y=a*cos(2*pi*60*ts1*n240);
subplot(312);
stem(n240,y);
xlabel('t');
ylabel('A');
title('discrete cos for sampling rate 240');
%________________________________________________________________________%
a=1;
t1000 = 0:1/1000:0.02;
n1000=0:(length(t1000)-1);
ts1=1/1000;
y=a*cos(2*pi*60*ts1*n1000);
subplot(313);
stem(n1000,y);
xlabel('t');
ylabel('A');
title('discrete cos for sampling rate 1000');
%________________________________________________________________________%

2. Output:-

3. clear
clc
%lab-4 part 2
% Practical : Exp-4 Title: Sampling Theorem
% Name: Omkar Rane
% Batch: 1 Block : 1
% Roll No: SETB118
% Seat No: S177086
%b). To comment on reconstructed signal while observing sampling signal.
%_________________________________________________________________________%
tf=0.05;
t=0:0.00005:tf;
f1=input('enter frequency 1 :');
f2=input('enter frequency 2 :');
f3=input('enter frequency 3 :');
fs=input('Enter Sampling frequency :');
ts=1/fs;
n=0:tf*fs;
q=n*ts;
xt1=cos(2*pi*f1*t);
xt2=cos(2*pi*f2*t);
xt3=cos(2*pi*f3*t);
xt=xt1+xt2+xt3;
xn=cos(2*pi*f1*q)+cos(2*pi*f2*q)+cos(2*pi*f3*q);
subplot(2,2,1);
plot(t,xt);
xlabel('t');
ylabel('A');
title('Original Continous Signal');
subplot(222);
stem(n,xn);
xlabel('t');
ylabel('A');
title('Discrete signal of original');

4. Output:

5. %lab-4 part 2
clear
clc
% Practical : Exp-4 Title: Sampling Theorem
% Name: Omkar Rane
% Batch: 1 Block : 1
% Roll No: SETB118
% Seat No: S177086
%c). To verify Nyquist criterion.
%_________________________________________________________%
tf=0.05;
t=0:0.00005:tf;
f1=input('enter frquency 1 :');
f2=input('enter frquency 2 :');
f3=input('enter frquency 3 :');
fs=input('Enter Sampling frequency :');
ts=1/fs;
n=0:tf*fs;
q=n*ts;
f=[f1 f2 f3];
fm=max(f);
xt1=cos(2*pi*f1*t);
xt2=cos(2*pi*f2*t);
xt3=cos(2*pi*f3*t);
xt=xt1+xt2+xt3;
xn=cos(2*pi*f1*q)+cos(2*pi*f2*q)+cos(2*pi*f3*q);
xa=xn*sinc(fs*(ones(length(n),1)*t-q'*ones(1,length(t))));

6. subplot(321);
plot(t,xt);
title('orignal signal');
subplot(322);
stem(q,xn);
title('sampled signal');
subplot(323);
plot(t,xa);
if fs<2*fm
title('reconstructed signal with sampling frequency
less than nyquist criteria ');
elseif fs==2*fm
title('rescontructed signal with sampling frequency
equal to nyquiest criteria');
else
title('Reconstructed signal with sampling frequency
greater than nyquist criteria');
end
Output: -
Condition when sampling frequency less than Nyquist criteria.

7. Output: -
Condition when sampling frequency equal to Nyquist criteria.
Condition when sampling frequency greater than Nyquist criteria.