dpnp.fft.ihfft

dpnp.fft.ihfft(a, n=None, axis=-1, norm=None, out=None)[source]

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

For full documentation refer to numpy.fft.ihfft.

Parameters:

  • a ({dpnp.ndarray, usm_ndarray}) -- Input array.

  • n ({None, 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. Default: None.

  • axis (int, optional) -- Axis over which to compute the FFT. If not given, the last axis is used. Default: -1.

  • norm ({None, "backward", "ortho", "forward"}, optional) -- Normalization mode (see dpnp.fft). Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor. None is an alias of the default option "backward". Default: "backward".

  • out ({None, dpnp.ndarray or usm_ndarray of complex dtype}, optional) -- If provided, the result will be placed in this array. It should be of the appropriate shape and dtype. Default: None.

Returns:

out -- 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.

Return type:

dpnp.ndarray of complex dtype

See also

dpnp.fft

For definition of the DFT and conventions used.

dpnp.fft.hfft

Compute the FFT of a signal that has Hermitian symmetry.

dpnp.fft.irfft

The inverse of dpnp.fft.rfft.

Notes

dpnp.fft.hfft/dpnp.fft.ihfft are a pair analogous to dpnp.fft.rfft/dpnp.fft.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 dpnp.fft.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 round-off error,

  • odd: ihfft(hfft(a, 2*len(a) - 1)) == a, within round-off error.

Examples

>>> import dpnp 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