Sampling

clear all
close all

t = 0 : 0.001 : 0.2 ;% time domain
f = 50 ;% cut off frequency
x = sin(2*pi*f.*t) ;% signal
Fs = 250 ;% sampling frequency
T = 0.004 ;% System produce a data for every 4ms.
plot(t,x);
hold on

for i = 0 : length(t)-1%% with this loop pulse train is procuded
if rem(i,4)==0
    pulse_train(i+1)=1;
else
    pulse_train(i+1)=0;
end
end
x1=x.*pulse_train;%%Signal and pulse train is multiplied
% and sampled datum assign to x1
stem(t,x1);%% The signal which has sampled datum is plotted.
% stem function is used for plot the discrete signals
j=1;
for i = 0 : length(t)-1
      % now with this loop we arease
         %the elements which are 0 in sampled signal
       
    if rem(i,4)==0
       x_discrete(j) = x1(i+1); 
       n(j) = t(i+1);
       j=j+1;
     end
end
figure(2);
stem(n,x_discrete);

%Sampling Frequencies
Fs1 = 75 ;
Fs2 = 250 ;
Fs3 = 5000 ;

%for different sampling frequency
%we create different time domain.

n1 = 0 : 1/Fs1 : 0.2 ;
n2 = 0 : 1/Fs2 : 0.2 ;
n3 = 0 : 1/Fs3 : 0.2 ;

Spline1 = interp1( n ,x_discrete ,n1 ,'spline' ) ;
Spline2 = interp1( n ,x_discrete ,n2 ,'spline' ) ;
Spline3 = interp1( n ,x_discrete ,n3 ,'spline' ) ;
% By increasing sampling frequency we can obtain
% our original signal as almost exactly the same.
figure(3);
subplot(311); plot(n1,Spline1);
subplot(312); plot(n2,Spline2);
subplot(313); plot(n3,Spline3);

N=1024;
fftx1=abs(fftshift(fft(Spline1,N))/N);
fftx2=abs(fftshift(fft(Spline2,N))/N);
fftx3=abs(fftshift(fft(Spline3,N))/N); 

f1=linspace(-Fs1/2,Fs1/2,1024);
f2=linspace(-Fs2/2,Fs2/2,1024);
f3=linspace(-Fs3/2,Fs3/2,1024);

figure(4);
subplot(311); plot(f1,fftx1);
subplot(312); plot(f2,fftx2);
subplot(313); plot(f3,fftx3);