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# numpy.fft.ihfft

fft.ihfft(a, n=None, axis=-1, norm=None, out=None)

  Compute the inverse FFT of a signal that has Hermitian symmetry.

  Parameters:
    a array_like

      Input array.

    n int, optional

      Length of the inverse FFT, the number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

    axis int, optional

      Axis over which to compute the inverse FFT. If not given, the last axis is used.

    norm{“backward”, “ortho”, “forward”}, optional

      Normalization mode (see `numpy.fft`). Default is “backward”. Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

      Added in version 1.20.0: The “backward”, “forward” values were added.

    out complex ndarray, optional

      If provided, the result will be placed in this array. It should be of the appropriate shape and dtype.

      Added in version 2.0.0.

  Returns:
    out complex ndarray

      The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. The length of the transformed axis is `n//2 + 1`.

  See also

  `hfft`, `irfft`

  Notes

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

  - even: `ihfft(hfft(a, 2*len(a) - 2)) == a`, within roundoff error,

  - odd: `ihfft(hfft(a, 2*len(a) - 1)) == a`, within roundoff error.

  Examples

      >>> import numpy as np
      >>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
      >>> np.fft.ifft(spectrum)
      array([1.+0.j,  2.+0.j,  3.+0.j,  4.+0.j,  3.+0.j,  2.+0.j]) # may vary
      >>> np.fft.ihfft(spectrum)
      array([ 1.-0.j,  2.-0.j,  3.-0.j,  4.-0.j]) # may vary