how to get frequency of a discrete signal by using fft in matlab

i want to find the frequency of a discrete signal using matlab and also want to apply a bandpass filter to that spectrum how can i do that pls help me out guys!!!

Answer 1

[Wayne King]

You identify the peak in the Fourier transform, find the index in DFT vector corresponding to that peak and relate that to frequency.

For example:

   % sampling frequency is 1 kHz
   Fs = 1000;
   % I'll create a signal consisting of a 100 Hz sine wave in noise
   t = 0:0.001:1-0.001;
   x = cos(2*pi*100*t)+randn(size(t));
   xdft = fft(x);
  % I only need to search 1/2 of xdft for the max because x is real-valued
   xdft(1:length(x)/2+1);
   [Y,I] = max(abs(xdft));
   freq = 0:Fs/length(x):Fs/2;
   fprintf('Maximum occurs at %3.2f Hz\n.',freq(I))

Note that the frequency bins in the DFT are spaced at Fs/N where Fs is the sampling frequency and N is the length of the signal. The first DFT "bin" corresponds to zero frequency.

Your next step is to construct a bandpass filter around 1 kHz, you can do that a number of ways in MATLAB. See fdesign.bandpass for example.

[newbie traveller]

ok sir .....thank you very much! but i need to know somethg more silly from you......the thing that you have did to find from 1/2 of xdft .......

xdft(1:length(x)/2+1);

[Y,I] = max(abs(xdft));

freq = 0:Fs/length(x):Fs/2;

fprintf('Maximum occurs at %3.2f Hz\n.',freq(I))

can pls explainn that more easily seems confusing to me ...pls explain me that more theoritically so that i can also do with my own !!!

as i know fft doesn't give me the real spectrum of a signal i have to do the fftshift to get the real one ....i just know these things so it would be better to make me understand further .it will probably help me ...thank you very much sir!

Answer 2

[Wayne King]

You don't have to do fftshift() to get the real spectrum. fftshift just puts 0 in the center with "negative" frequencies to the left and "positive" frequencies to the right. That is convenient in many applications, but not necessary.

If the signal is real-valued (not complex-valued), then a symmetry will exist between the two halfs of the Fourier transform. Therefore, in order to identify the peak frequency, you only need to work with 1/2 of the result.