# how can find frequency from an fft function?

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mrkovi on 22 Nov 2015
Edited: Ullah Nadeem on 18 Mar 2022
hi, I'm doing a coupled oscillators experiment involving two measured angles changing over time. i imported the data -csv - with one column (867x1) for each variable; time, angle 1, angle 2.
when i enter: plot(abs(fftshift(fft(Y1)))); (where Y1 = the column vector for angle 1.) i am unsure of the meaning of the figure that is produced, specifically the numbers on the x axis.
i have been told that the y axis is the amplitude and that the x axis is the index, but i do not understand how i am meant to understand the frequency of the oscillation from these two things.
additionally every post i have found connected to this problem refers to the following equation: Frequency = i * (Fs/N)
am i correct in assuming that "i" is the x coordinate? that N is 867? and Fs i am entirely confused as to how to calculate.

Rick Rosson on 23 Nov 2015
Edited: Rick Rosson on 23 Nov 2015
Fs = 40; % samples per second
N = length(Y1); % samples
dF = Fs/N; % hertz per sample
f = -Fs/2:dF:Fs/2-dF + (dF/2)*mod(N,2); % hertz
Y1_fft = fftshift(fft(Y1))/N;
figure;
plot(f,abs(Y1_fft));
Ullah Nadeem on 18 Mar 2022
Edited: Ullah Nadeem on 18 Mar 2022
Hello Rick!
Hope you're fine, I guess dF = Fs/N is hertz {(samples per sec)/(samples) = 1/sec = hertz} not hertz per sample, hertz per sample would be dF/N. Please correct me if I'm wrong...
Thank you!

Guillaume on 22 Nov 2015
It sounds like you're lacking the basics of fourier transform analysis. You would probably better off learning about it before trying to apply it.
Yes, i is your sample number, your x, axis. N is the number of sample (usually you try to make it a power of 2). Fs is your sampling frequency. You must have acquired your measurement at a fixed frequency.
##### 2 CommentsShowHide 1 older comment
Guillaume on 23 Nov 2015
Your sampling frequency is thus 40 Hz (40 samples per second).

Star Strider on 22 Nov 2015
The current R2015b documentation is confusing (at least in my opinion). See the R2015a documentation for fft for a more appropriate implementation. The only correction that needs to be made to the code between the first two plot figures is to multiply the result of the fft by 2 with a one-sided fft.
This will give the correct amplitudes:
Y = fft(y,NFFT)*2/L;

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