bundles / numpy latest / numpy / fft / irfft
_ArrayFunctionDispatcher
numpy.fft:irfft
source: build-install/usr/lib/python3.14/site-packages/numpy/fft/_pocketfft.py :421
Signature
def irfft ( a , n = None , axis = -1 , norm = None , out = None ) Summary
Computes the inverse of rfft.
Extended Summary
This function computes the inverse of the one-dimensional n-point discrete Fourier Transform of real input computed by rfft. In other words, irfft(rfft(a), len(a)) == a to within numerical accuracy. (See Notes below for why len(a) is necessary here.)
The input is expected to be in the form returned by rfft, i.e. the real zero-frequency term followed by the complex positive frequency terms in order of increasing frequency. Since the discrete Fourier Transform of real input is Hermitian-symmetric, the negative frequency terms are taken to be the complex conjugates of the corresponding positive frequency terms.
Parameters
a: array_likeThe input array.
n: int, optionalLength of the transformed axis of the output. For
noutput points,n//2+1input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. Ifnis not given, it is taken to be2*(m-1)wheremis the length of the input along the axis specified byaxis.axis: int, optionalAxis over which to compute the inverse FFT. If not given, the last axis is used.
norm: {"backward", "ortho", "forward"}, optionalNormalization mode (see numpy.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.
out: ndarray, optionalIf provided, the result will be placed in this array. It should be of the appropriate shape and dtype.
Returns
out: ndarrayThe truncated or zero-padded input, transformed along the axis indicated by
axis, or the last one ifaxisis not specified. The length of the transformed axis isn, or, ifnis not given,2*(m-1)wheremis the length of the transformed axis of the input. To get an odd number of output points,nmust be specified.
Raises
: IndexErrorIf
axisis not a valid axis ofa.
Notes
Returns the real valued n-point inverse discrete Fourier transform of a, where a contains the non-negative frequency terms of a Hermitian-symmetric sequence. n is the length of the result, not the input.
If you specify an n such that a must be zero-padded or truncated, the extra/removed values will be added/removed at high frequencies. One can thus resample a series to m points via Fourier interpolation by: a_resamp = irfft(rfft(a), m).
The correct interpretation of the hermitian input depends on the length of the original data, as given by n. This is because each input shape could correspond to either an odd or even length signal. By default, irfft assumes an even output length which puts the last entry at the Nyquist frequency; aliasing with its symmetric counterpart. By Hermitian symmetry, the value is thus treated as purely real. To avoid losing information, the correct length of the real input must be given.
Examples
import numpy as np
✓np.fft.ifft([1, -1j, -1, 1j]) np.fft.irfft([1, -1j, -1])✗
See also
Aliases
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numpy.fft.irfft