## Using fft() to calculate PSD.

on 21 Jun 2012

### Wayne King (view profile)

I used the code below perform spectral analysis of signal with known period of 4 s:
data_out.time = lujan(:,1);
data_out.disp = lujan(:,2);
Y = fft(data_out.disp,1000);
Y(1)=[];
NY = length(Y);
Pyy = abs(Y(1:floor(NY/2))).^2;
nyquist = 1/2;
f = (1:NY/2)/(NY/2)*nyquist;
plot(f,Pyy,'-b','LineWidth',3);
title('Power spectral density');
xlabel('Frequency (Hz)');
However the output graph shows a peak at 0.05 Hz which is not correct! IS there something obvious i'm doing wrong?
thanks

### Wayne King (view profile)

on 21 Jun 2012

Are you sure the sampling frequency is 1 ? If so, how far off is the peak from where you expect it to be? Is it almost correct or way off? You also don't tell us how long the time series is, so we don't know why you are adding the length input argument to fft() . Your frequency increment of 1/NY (0.0025) is correct.

2one

### 2one (view profile)

on 21 Jun 2012
the signal is from 0 to 12 sec, sampled every 0.2 sec (61 points total).
the signal has period of 4 s so frequency peak should be at 0.25 hZ but graph is showing peak at 0.05 Hz (which would mean 20 s period).

### Wayne King (view profile)

on 21 Jun 2012

Then your sampling frequency is specified incorrectly.
Fs = 1/0.2;
% here I'll create a signal just to show you
t = 0:1/Fs:12-1/Fs;
x = cos(2*pi*0.25*t)+randn(size(t));
Y = fft(x,256);
Pyy = abs(Y(1:floor(256/2)+1)).^2;
freq = 0:Fs/256:5/2;
plot(freq,10*log10(Pyy))
grid on
set(gca,'xtick',[0 0.25 0.5 1 1.5 2 2.5])