What Is Wrong With My Code? (Downsampling Of A Sinc Signal)

Hi, I'm studying on my own about downsampling the signals on matlab.

Before exhibit my code which I wrote, I've curiosity questions below about my code.

I'm a self learner, so if anyone else could help me to understand. That would be glamorous.

1) How can I find the downsampling of my code?

2) How can I create a discrete time sinusoidal signal of a preferred frequency and decimate it?

Here is my code mentioned before which I wrote it:

N = 30; 
n= 0:N; 
x1 = sinc(n/6); 
subplot(221);
stem(n,x1); 
grid; 
title('original signal');
xlabel('sample');

m = 2;
x2 = x1(1:m:length(x1));
m = 0:m:N; 
subplot(222);
stem(m,x2); 
grid; 
title('decimated signal');
xlabel('sample');

f1=0:0.1:3;    %frequency values 
f2=0:0.4:6;    %new frequency values

X1 = abs(fft(x1)); 
subplot(223);
stem(f1,X1);
title('input spectrum');
xlabel('frequency(Hz)'); 

X2 = abs(fft(x2));
subplot(224);
stem(f2,X2);
title('output spectrum');
xlabel('frequency(Hz)');

Here is my output:

Answer 1

[Paul]

Hi @cikalekli,

I'm not sure what you're trying to show, but I can see at least one issue in the code that needs to be considered. Maybe looking for something like this:

N = 30;         % Length of the original sequence
n = 0:N-1;      % note the N-1 so that n has 30 samples  
x1 = sinc(n/6); % define the original sequence
Fs = 3;         % it looks like this should be the sampling frequency 

subplot(231);
stem(n,x1); 
grid; 
title('original signal');
xlabel('sample');

M = 2;     % downsampling factor
x2 = x1(1:M:length(x1));  % the downsampled signal. Could also use x2 = downsample(x1,M)

Up to this point, there are no problems. However, the next line is problematic. In discrete time the independent variable has to cover all integers, but this definition of the values of m that correspond to the values of x2 are only even values of the independent variable, which is against the rules so to speak

m = 0:M:N;  

After downsampling, the indices the correspond to x2 are really

m = 0:(numel(x2)-1);

and it is the indices of m as defned here that will be used in the DFT computation in fft(x2).

subplot(232);
stem(m,x2); 
grid; 
title('decimated signal');
xlabel('sample');

Now we can go to the frequency domain

X1 = abs(fft(x1));
f1 = (0:numel(X1)-1)/numel(X1)*Fs;
subplot(234);
stem(f1,X1);
title('input spectrum');
xlabel('frequency(Hz)');

X2 = abs(fft(x2));
f2 = (0:numel(X2)-1)/numel(X2)*Fs/M; % by downsampling, we increased the sampling period, which decreases the sampling frequency
subplot(235);
stem(f2,X2);
title('output spectrum');
xlabel('frequency(Hz)');

Now, we can upsample the down-sampled signal

x3 = upsample(x2,M);
subplot(233)
stem(n,x3);
grid
xlabel('sample')
title('upsampled output')

And its DFT

X3 = abs(fft(x3));
f3 = f1;
subplot(236)
stem(f3,X3);
xlabel('frequency(Hz)')
title('upsampled spectrum')