# Sampling and recovery using matlab

I'm trying to write a program using MATLAB that samples and recovers a given signal with different sampling frequencies

The given signal is $x(t) = \sin (2\pi 200 t)$ and sampling frequencies are $200$,$300$,$400$ and $500$ Hz.

I used sinc interpolation formula.

It is not working,and I would like to know why.

Can you help me?

The code is:

 f=200;
fs=[200,300,400,500]; % sampling frequencies
for i = 1:length(fs)

Ts = 1/fs(i); % Sampling Period
t = 0:1e-4:6/f; % time vector for continous plot
w = f*2*pi;
xa = sin(w*t); % signal in continuous form

t2=(0:Ts:6/f);  % time vector for sampling
xb = sin(w*t2); % sampled signal

figure
subplot(311);
plot(t,xa) % continous signal plot
str = ['Signal x(t) = (' num2str(f) ' Hz)', ', Fs = ' num2str(fs(i)) ' Hz'];
title(str);
ylabel('Amplitude');
xlabel('Time(s)');

subplot(312);

stem(t2,xb); % sampled signal plot
title('Sampled signal');
ylabel('Amplitude')
xlabel('Samples');

xr = zeros(length(t));
for k=1:length(t)
for p=1:length(xb)
xr(k)=xr(k) + xb(p)*sinc(fs(i)*(k-t2(p)));
end
end
subplot(313);
plot(t,xr);
title('Recovered signal');
ylabel('Amplitude');
xlabel('Time(s)');
end

• Haven't looked at your code, but here's something similar: mathworks.com/matlabcentral/fileexchange/… Sep 8 '17 at 21:05
• Those sampling frequencies will create aliasing except for $f_s=500$ Hz. I hope you're aware of this and know what you should expect. Sep 8 '17 at 21:12
• I'm aware of that,but recovered signal is weird even with 500hz sampling Sep 8 '17 at 21:22
• Hi Mateus, if you got an answer to your question (it looks like you did), please consider accepting it.
– jojek
Jan 15 '18 at 11:26

This line is wrong:

xr(k)=xr(k) + xb(p)*sinc(fs(i)*(k-t2(p)));


The correct one is:

xr(k)=xr(k) + xb(p)*sinc( ((k-1)*Tr-(p-1)*Ts)/Ts );


Where $Ts$ is the original sampling period and $Tr$ is the reconstruction sampling period. In your code $Ts$ is given by $T_s = 1/500$ for sampling frequency of $500$ Hz. And $T_r = 10^{-4}$ set by your continuous plot period.

Note that you will still have slight errors due to the fact that the input signal is not being perfectly bandlimited.

Here is the resulting plot for $Fs=500$ Hz, $f_0 = 200$ Hz and $T_r=10^{-4}$ seconds: it's ok now.

• you may accept the answer if it worked for you... Sep 8 '17 at 22:00
• It sure has! Thank you so much! Sorry for my delay! Sep 10 '18 at 10:23