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# numpy.fft.hfft

`numpy.fft.``hfft`(a, n=None, axis=-1)

  Compute the FFT of a signal whose spectrum has Hermitian symmetry.

  Parameters : | a : array_like The input array. n : int, optional The length of the FFT. axis : int, optional The axis over which to compute the FFT, assuming Hermitian symmetry of the spectrum. Default is the last axis.
  Returns : | out : ndarray The transformed input.

  See also

  `rfft`
    Compute the one-dimensional FFT for real input.
  `ihfft`
    The inverse of `hfft`.

  Notes

  `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the opposite case: here the signal is real in the frequency domain and has Hermite symmetry in the time domain. So here it’s `hfft` for which you must supply the length of the result if it is to be odd: `ihfft(hfft(a), len(a)) == a`, within numerical accuracy.

  Examples

      >>> signal = np.array([[1, 1.j], [-1.j, 2]])
      >>> np.conj(signal.T) - signal   # check Hermitian symmetry
      array([[ 0.-0.j,  0.+0.j],
             [ 0.+0.j,  0.-0.j]])
      >>> freq_spectrum = np.fft.hfft(signal)
      >>> freq_spectrum
      array([[ 1.,  1.],
             [ 2., -2.]])