Return value of fft function and details of the bins

Question

Mahesh 2014-1-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/112356-return-value-of-fft-function-and-details-of-the-bins

编辑： Wesley Ooms 2014-2-3

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

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Wesley Ooms 2014-1-14

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/112356-return-value-of-fft-function-and-details-of-the-bins#answer_120871

编辑：Wesley Ooms 2014-2-3

在 MATLAB Online 中打开

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),'.')

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Wesley Ooms 2014-1-14

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

请先登录，再进行评论。

Answer 2

Matt J 2014-1-14

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/112356-return-value-of-fft-function-and-details-of-the-bins#answer_120856

编辑：Matt J 2014-1-14

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.

2 个评论
显示无隐藏无

Mahesh 2014-1-14

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 2014-1-14

编辑：Matt J 2014-1-14

在 MATLAB Online 中打开

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).

请先登录，再进行评论。