define frequency of signal from fft output

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what is the relationship between the sampling frequency Fs and frequency of signal of FFT function in matlab? assUme that, we have a signal with spectrum as follow picture. with Fs= 44.1Khz, I know that X-axis is not the frequecy of signal, right? How to define the frequency of this signal with followed spectrum? for example, at the point X-axis = 10000, with Fs= 44.1Khz, how to define frequency of signal at that point?

Accepted Answer

Rick Rosson
Rick Rosson on 29 Sep 2014
Edited: Rick Rosson on 29 Sep 2014
dF = Fs/N;
f = dF*(0:N-1)';

More Answers (4)

Ngoc Lam
Ngoc Lam on 30 Sep 2014
Edited: Ngoc Lam on 30 Sep 2014
thanks for your opinions! it's helpful for me! But I have a trouble with using fft for analysing spectrum of signals. for example we have a code segment:
%%%% code segment %%%%
t= linspace (0,4*pi,500);
x= sin(100*pi*t)+2*cos(200*pi*t);
X= abs(fft(x));
%%%%%%%%%
with followed picture representing the spectrum of that picture.
  • *
how we can define frequency of any point in X-axis?
at point (125) in X-axis, how can we determine the frequency of that signal at that point?
thanks!* *
  1 Comment
Rick Rosson
Rick Rosson on 30 Sep 2014
The sampling rate in your code is
Fs = 500/(4*pi);
which is approximately 40 samples per second. By the Nyquist Sampling Theorem, the maximum frequency that you can represent without aliasing is Fs/2 or approx 20 Hertz. Your signal, however, contains components at 50 Hertz and 100 Hertz, which are well above the maximum.

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Rick Rosson
Rick Rosson on 30 Sep 2014
Please try:
Fs = 1000;
dt = 1/Fs;
N = 12000;
t = dt*(0:N-1)';
x = sin(100*pi*t) + 2*cos(200*pi*t);
X = fftshift(fft(x))/N;
dF = Fs/N;
f = -Fs/2:dF:Fs/2-dF;
plot(f,abs(X));
  1 Comment
Syed Masoud Shah kakakhel
Syed Masoud Shah kakakhel on 23 Mar 2017
Edited: Syed Masoud Shah kakakhel on 23 Mar 2017
kindly @Rick Rosson can u comment...variables like what is N?? kindly will be more helpful..m waiting for response

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Ngoc Lam
Ngoc Lam on 1 Oct 2014
Ah, I have no pay attention to Nyquyst sampling theorem aplied here! I have solved my problems, thanks for your help!

Ngoc Lam
Ngoc Lam on 1 Oct 2014
Do you know the meaning of the symmetry of spectrum when we plot spectrum of signal?
i thought that It's the negative spectrum of signal? Is it right?

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