irfft(a, n=None, axis=-1, norm=None)
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.
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.
The input array.
Length of the transformed axis of the output. For n output points, n//2+1
input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. If n is not given, it is taken to be 2*(m-1)
where m
is the length of the input along the axis specified by :None:None:`axis`.
Axis over which to compute the inverse FFT. If not given, the last axis is used.
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.
The "backward", "forward" values were added.
If :None:None:`axis` is not a valid axis of a.
The truncated or zero-padded input, transformed along the axis indicated by :None:None:`axis`, or the last one if :None:None:`axis` is not specified. The length of the transformed axis is n, or, if n is not given, 2*(m-1)
where m
is the length of the transformed axis of the input. To get an odd number of output points, n must be specified.
Computes the inverse of rfft
.
fft
The one-dimensional FFT.
irfft2
The inverse of the two-dimensional FFT of real input.
irfftn
The inverse of the n-dimensional FFT of real input.
numpy.fft
For definition of the DFT and conventions used.
rfft
The one-dimensional FFT of real input, of which :None:None:`irfft` is inverse.
>>> np.fft.ifft([1, -1j, -1, 1j]) array([0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]) # may vary
>>> np.fft.irfft([1, -1j, -1]) array([0., 1., 0., 0.])
Notice how the last term in the input to the ordinary ifft
is the complex conjugate of the second term, and the output has zero imaginary part everywhere. When calling irfft
, the negative frequencies are not specified, and the output array is purely real.
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.fft.irfft
numpy.fft.irfftn
numpy.fft.rfft
numpy.fft.irfft2
numpy.fft.hfft
numpy.fft.ihfft
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