Power spectral density of a under sampled signal

Hi ,

I have a under sampled signal x. which is a 2k Hz signal. This same signal is under sampled at 50Hz. I tried to extract to freq response of this signal but as the siganl is sampled below the Nyquest rate I am not able to get it. I also tried with pwelch() function but it is also not giving me correct reasult.

How should I calculate the power spectral density of this signal x?

fs = 50
t = 0:1/fs:2^22- 1/fs;                 
x =  sin(2*pi*2000*t) ;
plot(t,x);
y = fft(x);     
f = (0:length(y)-1)*50/length(y)*80;
plot(f,abs(y))
title('Magnitude')

figure(2)
num_segments = 32;

window_length = floor(length(x)/num_segments);
[PSDphase ,f] =pwelch(x ,window_length ,[] ,[] ,50 ,'twosided');
h=semilogx( f, (10* log10(PSDphase)), 'b'); %hold on;
grid on;

Answer 1

[Navya Seelam]

Increase the sampling frequency of the signal to get expected results. When a signal is undersampled , aliasing happens and hence you are not able to get correct result.

[DIPAN KAR]

Dear,

Thank you for the answer. But in the actual problem I can't increase the sampling frequency. So is there a solution of this kind of problem when the sampling frequency is less than that signal frequency?

Regards

[Navya Seelam]

Hi,

One thing to notice here is the signal x is of the form sin(2*pi*n) with n being an integer. So x is actually a zero signal or nearly zero signal (due to precision limitations) and we cannot perform any operation on a zero signal.

[DIPAN KAR]

Thank you for pointing out the error. But I wanted to do fft of the phase and extract the PSD from it. Is this is the correct way?

fs = 50
t = 0:1/fs:2^22- 1/fs;                 
x =  2*pi*2000*t;
plot(t,x);
y = fft(x);     
f = (0:length(y)-1)*50/length(y)*80;
plot(f,abs(y))
title('Magnitude')
figure(2)
num_segments = 32;
window_length = floor(length(x)/num_segments);
[PSDphase ,f] =pwelch(x ,window_length ,[] ,[] ,50 ,'twosided');
h=semilogx( f, (10* log10(PSDphase)), 'b'); %hold on;
grid on;