How do I obtain the frequencies of each value in an FFT

Question

I have an FFT result  These are stored in two double arrays  a real part array and an imaginary part array  How do I determine the frequencies that correspond to each element in these arrays   In other words  I would like have create an array that stores the frequencies for each real and imaginary component of my FFT

User · Answer

I have used the following   public static double Index2Freq int i  double samples  int nFFT      return  double  i    samples   nFFT   2       public static int Freq2Index double freq  double samples  int nFFT      return  int   freq    samples   nFFT   2 0        The inputs are    i  Bin to access samples  Sampling rate in Hertz  i e  8000 Hz  44100Hz  etc   nFFT  Size of the FFT vector

User · Answer

Take a look at my answer here   Answer to comment   The FFT actually calculates the cross-correlation of the input signal with sine and cosine functions  basis functions  at a range of equally spaced frequencies   For a given FFT output  there is a corresponding frequency  F  as given by the answer I posted   The real part of the output sample is the cross-correlation of the input signal with cos 2 pi F t  and the imaginary part is the cross-correlation of the input signal with sin 2 pi F t    The reason the input signal is correlated with sin and cos functions is to account for phase differences between the input signal and basis functions     By taking the magnitude of the complex FFT output  you get a measure of how well the input signal correlates with sinusoids at a set of frequencies regardless of the input signal phase   If you are just analyzing frequency content of a signal  you will almost always take the magnitude or magnitude squared of the complex output of the FFT

User · Answer

The first bin in the FFT is DC  0 Hz   the second bin is Fs   N  where Fs is the sample rate and N is the size of the FFT  The next bin is 2   Fs   N  To express this in general terms  the nth bin is n   Fs   N   So if your sample rate  Fs is say 44 1 kHz and your FFT size  N is 1024  then the FFT output bins are at     0    0   44100   1024       0 0 Hz   1    1   44100   1024      43 1 Hz   2    2   44100   1024      86 1 Hz   3    3   44100   1024     129 2 Hz   4        5               511  511   44100   1024   22006 9 Hz   Note that for a real input signal  imaginary parts all zero  the second half of the FFT  bins from N   2   1 to N - 1  contain no useful additional information  they have complex conjugate symmetry with the first N   2 - 1 bins   The last useful bin  for practical aplications  is at N   2 - 1  which corresponds to 22006 9 Hz in the above example  The bin at N   2 represents energy at the Nyquist frequency  i e  Fs   2     22050 Hz in this example   but this is in general not of any practical use  since anti-aliasing filters will typically attenuate any signals at and above Fs   2

User · Answer

Your kth FFT result s frequency is 2 pi k N

User · Answer

The FFT output coefficients  for complex input of size N  are from 0 to N - 1 grouped as  LOW MID HI HI MID LOW  frequency   I would consider that the element at k has the same frequency as the element at N-k since for real data  FFT N-k    complex conjugate of FFT k    The order of scanning from LOW to HIGH frequency is  0    1   N-1    2   N-2          N 2  - 1   N -   N 2  - 1     N 2  1     N 2    There are  N 2  1 groups of frequency from index i   0 to  N 2   each having the frequency    i   SamplingFrequency   N  So the frequency at bin FFT k  is   if k  lt    N 2  then k   SamplingFrequency   N if k  gt    N 2  then  N-k    SamplingFrequency   N

[c#] How do I obtain the frequencies of each value in an FFT?

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