Return value of fft function and details of the bins

HI, I am a new to matlab and fft() .

Could you please help me in understudying the return value(data structure) of fft function in terms of the frequency bins. I was not able to find a proper explanation of bins .

regards Mahesh

Answer 1

[Wesley Ooms]

The bins are slightly different between even and odd number of sample points. I use the following:

 f     = ceil(-N/2:N/2-1)/dt/N ; % frequency points

where N is the number of sample points and dt sample time. You can check this with for example a multisinus with its frequency an integer number uf the base frequency and without a window:

 N     = 11112                     ; % number of samples
 dt    = 1e-4                      ; % sample time
 t     = dt*(0:N-1)                ; % time points
 f     = [-N/2:-1 ~odd(N):N/2]/dt/N; % frequency points
 freqs = f(f>100&f<1000)           ; % frequencys in the signal
 its   = 1:length(freqs)           ; % iterations
 phase = its.^2*pi/1e3             ; % phase of frequencys in the signal (schroeder phase)
 a     = 0                         ; % DC offset

 for i=its
     a=a+cos(2*pi*freqs(i)*t+phase(i));
 end

 b=fftshift(fft(a));

 subplot(311),plot(t,a       ,'-')
 subplot(312),plot(f,abs  (b),'.')
 subplot(313),plot(f,angle(b),'.')

[Wesley Ooms]

If ~odd(N) doesn't work, you van use 1-rem(N,2) or 1-mod(N,2).

Answer 2

[Matt J]

If you are sampling time at intervals T seconds, the frequency samples will be (k-1)/(N*T) Hz, where k=1,...,N and X(k) is the output of your fft.

[Mahesh]

Thanks Matt. I have some more doubts . If I am taking samples with 512 samples per second . and do fft for a one second signal . fft will return me 512 bins.Could you please let me know whether my understanding is correct .

returned bins will contain 1/2 the details of frequency components with maximum 1/2 the sampling frequency . first 256 bins will contain real part of the frequency component . Next 256 will contain the imaginary part ? My confusion is how this will be ordered in the bin

[Matt J]

Yes, the fft will return 512 bins spaced apart by 1 Hz. The first half of the samples will correspond to positive frequencies in the continuous Fourier domain and the second half of the samples will be negative frequencies.

If you apply fftshift() to the output of fft then the samples will be re-ordered so that negative frequencies are on the left. The corresponding continuous space frequency sample axis will then be,

 frequencyAxis= ((0:N-1) -ceil((N-1)/2))*Fs/N;

i.e., with DC at frequencyAxis(257).