nlcpy.fft.ihfft

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

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

Parameters

aarray_like: Input array.
nint, 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.
axisint, optional: Axis over which to compute the inverse FFT. If not given, the last axis is used.
norm{None, “ortho”},optional: Normalization mode. By default(None), the transforms are scaled by $1/n$ . It norm is set to “ortho”, the return values will be scaled by $1/\sqrt{n}$ .

Returns

outcomplex 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: Computes the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
irfft: Computes the inverse FFT of a signal that has Hermitian symmetry.

Note

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