Help with FFT and Dominant Frequency

Hi Everyone,

I'm trying to find dominant frequency using FFT? However, for a vector array which spikes at every 10th iteration and is 0 for everywhere else, I get spikes every 10Hz after I plot FFT data vs. frequency. The pseudo code is

clear all close all clc

%%

fs = 100; % Frequcny of Image Acquisition, 100 Hz T = 1; % Total Time t = 1/fs:1/fs:T; % Time Vector

x = [0,0,0,0,0,0,0,0,0,1,... 0,0,0,0,0,0,0,0,0,0.5,... 0,0,0,0,0,0,0,0,0,.7,... 0,0,0,0,0,0,0,0,0,.8,... 0,0,0,0,0,0,0,0,0,.6,... 0,0,0,0,0,0,0,0,0,.4,... 0,0,0,0,0,0,0,0,0,.8,... 0,0,0,0,0,0,0,0,0,.85,... 0,0,0,0,0,0,0,0,0,1,... 0,0,0,0,0,0,0,0,0,1]; % Image Intensity vector

figure plot(t,x) xlabel('Time, (s)') ylabel ('Image Intensity')

%% Fourier

m = length(x); n = pow2(nextpow2(m)); dim = 2; y = fft(x,n, dim); f = (0:n-1)*(fs/n);

p = y.*conj(y)/n; % figure % plot (f,p) figure plot(f(1:n/2), p(1:n/2)) xlabel('Frequency, (Hz)') ylabel ('P(f)')

Is there something wrong with the code? My understanding is that FFT should only return the dominant frequency, which is 10Hz in this case. Thanks Saad

Answer 1

[David Goodmanson]

Hi Saad,

The fft of a pulse train of uniform spikes is another pulse train of uniform spikes, not just a spike at a single frequency. For example,

n = 200;
y = zeros(1,n);
y(10:10:200) = 1;     % exactly periodic
figure(1)
plot(y)
z = fft(y);
figure(2)
plot(1:n,abs(z),1:n,angle(z))

gives another uniform pulse train. [ Technically I suppose the new pulse train z is not uniform, because each pulse is multiplied by a phase factor, but those just have to do with a translation of the original pulse train y. If everything in y is shifted so that the first spike occurs at the beginning of the y array then there are no extra phase factors in z ]

Your input data does not have constant-height pulses so you get the pulse train with some extra, smaller stuff as well.

OK, here comes my rant for the day. Upon running this code,

n = 200;
y = zeros(1,n);
y(10:10:200) = 1;
n1 = pow2(nextpow2(length(x)));
z = fft(y,n1);
figure(2)
plot(1:n1,abs(z),1:n1,angle(z))

then compared to the original code you get a bunch of slop for the fft. In the first case the y waveform is truly periodic, because the pulse spacing of 20 exactly divides the array length of 200. So if another copy of the y array is appended on the right, it looks the same (only twice as long). But power-of-2 appends zeros to the y array, changes its length and messes up the periodicity. I think that the power-of-2 thing is way overvalued and far too often misapplied.