Code-m file for Sampling

Write a MATLAB code to

1) Generate a band limited signal (at extremely high sampling rate to approximate it as a continuous signal)

2) Plot the signal in Time Domain.

3) Take the FFT of the signal and plot the magnitude and phase of the signal spectrum and show it is a bandlimited signal.

4) Generate an impulse train at an appropriate sampling rate using DFS and show that its FFT is again an impulse train.

5) Using the signal and impulse train generated in (1) and (4), produce sampled signal by multiplying the two and apply FFT.

6) Display the sampled signal and its spectrum.

7) Reconstruct the original signal from its sampled value using sinc (interpolation) filter and display the same.

Answer 1

[VBBV]

clear all
close all
% Creating modulating signal
fm=2; % message signal frequency (Hz)
n=50; % factor of sampling frequency
K=1000;
Ts=1/(n*fm); % sampling time
t=0:Ts:100-Ts; % time range
N=size(t,2);
Fs=1/Ts; % sampling frequency
dFs=Fs/N;
f=-Fs/2:dFs:Fs/2-dFs;
m=2*cos(2*pi*fm*t); % message signal
subplot(5,1,1);
plot(t,m);
xlabel('Time(in s)');
title('Modulating signal');
% Frequency Domain
M=fftshift(fft(m)); % FFT of the message signal
subplot(5,1,2)
plot(f,abs(M)/N);
xlabel('Frequency(in hertz)');
title('Magnitude response');
%sound(X)
% Pulse train generation
T=0.2; %sampling interval
F=1/T; % sapling frequency
h=zeros(1,length(t)); % initialize all values to zero
for k=-K:1:K
h=h+(1/T)*cos(2*pi*k*F*t);
end
h_a=T*h/(2*K+1); % scaling 
subplot(5,1,3);
plot(t,h_a);
xlabel('Time(s)');
title('Pulse train');
% sampling
m_samp=m.*h_a;
N_samp=length(m_samp);
subplot(5,1,4); 
plot(t,m_samp);% add the plot function 
xlabel('Time(in s)');
title('Sampled value');
% Magnitude response of sampled signal
M_samp=fftshift(fft(m_samp)); 
subplot(5,1,5)
plot(f,abs(M_samp)/N_samp);
xlabel('Frequency(in hertz)');
title('Magnitude response')

You forgot to use plot function. Check with this

m_samp=m.*h_a;
N_samp=length(m_samp);
subplot(5,1,4); 
plot(t,m_samp);% add the plot

[VBBV]

M_samp=fftshift(fft(m_samp)); 
H = sinc(M_samp)./N_samp;
G = filter(H,1,t); 
plot(f,G)

Add this to reconstruct the sampled signal

[Sushilkumar]

% Sampling Theorem
clc;
clear all;
t = -100:0.01:100;
T=30;
fm = 1/T;
x = cos(2*pi*fm*t);
subplot(2,2,1);
plot(t,x);
grid on;
xlabel('Time in seconds');
xlabel('x(t)');
title('Continuous time signal');
fs1 = 1.6*fm;
n1 = -5:1:5;
xn1 = cos(2*pi*n1*fm/fs1);
subplot(2,2,2);
stem(n1,xn1);
hold on;
plot(n1, xn1);
grid on;
xlabel('Time in seconds');
xlabel('x(t)');
title('Discrete time signal with fs1<2fm');
fs2 = 2*fm;
n2 = -5:1:5;
xn2 = cos(2*pi*n2*fm/fs2);
subplot(2,2,3);
stem(n2,xn2);
hold on;
plot(n2, xn2);
grid on;
xlabel('Time in seconds');
xlabel('x(t)');
title('Discrete time signal with fs2 = 2fm');
fs3 = 8*fm;
n3 = -20:1:20;
xn3 = cos (2*pi*n3*fm/fs3);
subplot(2,2,4);
stem(n3,xn3);
hold on;
plot(n3, xn3);
grid on;
xlabel('Time in seconds');
xlabel('x(t)');
title('Discrete time signal with fs1 > 2fm');



sampling 

Answer 2

[Sulaymon Eshkabilov]

Could pl., show what you have done so far?

[Chetan Fadnis]

% Sampling and Reconstruction

clc

clear all

close all

% Creating modulating signal

fm=2; % message signal frequency (Hz)

n=50; % factor of sampling frequency

K=1000;

Ts=1/(n*fm); % sampling time

t=0:Ts:100-Ts; % time range

N=size(t,2);

Fs=1/Ts; % sampling frequency

dFs=Fs/N;

f=-Fs/2:dFs:Fs/2-dFs;

m=2*cos(2*pi*fm*t); % message signal

subplot(5,1,1);

plot(t,m);

xlabel('Time(in s)');

title('Modulating signal');

% Frequency Domain

M=fftshift(fft(m)); % FFT of the message signal

subplot(5,1,2)

plot(f,abs(M)/N);

xlabel('Frequency(in hertz)');

title('Magnitude response');

%sound(X)

% Pulse train generation

T=0.2; %sampling interval

F=1/T; % sapling frequency

h=zeros(1,length(t)); % initialize all values to zero

for k=-K:1:K

h=h+(1/T)*cos(2*pi*k*F*t);

end

h_a=T*h/(2*K+1); % scaling

subplot(5,1,3);

plot(t,h_a);

xlabel('Time(s)');

title('Pulse train');

% sampling

m_samp=m.*h_a;

N_samp=length(m_samp);

subplot(5,1,4);

xlabel('Time(in s)');

title('Sampled value');

% Magnitude response of sampled signal

M_samp=fftshift(fft(m_samp));

subplot(5,1,5)

plot(f,abs(M_samp)/N_samp);

xlabel('Frequency(in hertz)');

title('Magnitude response')

Finding difficulty in Reconstruction part

Answer 3

[Adel]

clear all

close all

% Creating modulating signal

fm=2; % message signal frequency (Hz)

n=50; % factor of sampling frequency

K=1000;

Ts=1/(n*fm); % sampling time

t=0:Ts:100-Ts; % time range

N=size(t,2);

Fs=1/Ts; % sampling frequency

dFs=Fs/N;

f=-Fs/2:dFs:Fs/2-dFs;

m=2*cos(2*pi*fm*t); % message signal

subplot(5,1,1);

plot(t,m);

xlabel('Time(in s)');

title('Modulating signal');

% Frequency Domain

M=fftshift(fft(m)); % FFT of the message signal

subplot(5,1,2)

plot(f,abs(M)/N);

xlabel('Frequency(in hertz)');

title('Magnitude response');

%sound(X)

% Pulse train generation

T=0.2; %sampling interval

F=1/T; % sapling frequency

h=zeros(1,length(t)); % initialize all values to zero

for k=-K:1:K

h=h+(1/T)*cos(2*pi*k*F*t);

end

h_a=T*h/(2*K+1); % scaling

subplot(5,1,3);

plot(t,h_a);

xlabel('Time(s)');

title('Pulse train');

% sampling

m_samp=m.*h_a;

N_samp=length(m_samp);

subplot(5,1,4);

plot(t,m_samp);% add the plot function

xlabel('Time(in s)');

title('Sampled value');

% Magnitude response of sampled signal

M_samp=fftshift(fft(m_samp));

subplot(5,1,5)

plot(f,abs(M_samp)/N_samp);

xlabel('Frequency(in hertz)');

title('Magnitude response')