# Power spectral density of a under sampled signal

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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;

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### Answers (1)

Navya Seelam
on 12 May 2020

##### 3 Comments

Navya Seelam
on 14 May 2020

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.

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