flopscope.

flopscope.numpy.fft.ihfft

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

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

Adapted from NumPy docs np.fft.ihfft

Areafft
Typecustom
NumPy Refnp.fft.ihfft
Cost
5n⋅⌈log⁡2n⌉5n \cdot \lceil\log_2 n\rceil
Flopscope Context

Inverse FFT of Hermitian signal. Cost: 5*n*ceil(log2(n)) (Cooley-Tukey radix-2; Van Loan 1992 §1.4).

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 flops.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.
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

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