define frequency of signal from fft output

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?

Answer 1

[Rick Rosson]

   dF = Fs/N;
   f = dF*(0:N-1)';

[YAMASANI MANOJ REDDY]

what for dct

Answer 2

[Ngoc Lam]

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!* *

[Rick Rosson]

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.

Answer 3

[Rick Rosson]

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));

[Syed Masoud Shah kakakhel]

kindly @Rick Rosson can u comment...variables like what is N?? kindly will be more helpful..m waiting for response

Answer 4

[Ngoc Lam]

Ah, I have no pay attention to Nyquyst sampling theorem aplied here! I have solved my problems, thanks for your help!

Answer 5

[Ngoc Lam]

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?