numpy.fft.irfft¶

numpy.fft.
irfft
(a, n=None, axis=1, norm=None)[source]¶ Compute the inverse of the npoint DFT for real input.
This function computes the inverse of the onedimensional npoint 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 whylen(a)
is necessary here.)The input is expected to be in the form returned by
rfft
, i.e. the real zerofrequency term followed by the complex positive frequency terms in order of increasing frequency. Since the discrete Fourier Transform of real input is Hermitiansymmetric, the negative frequency terms are taken to be the complex conjugates of the corresponding positive frequency terms.Parameters:  a : array_like
The input array.
 n : int, optional
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 be2*(m1)
wherem
is the length of the input along the axis specified by axis. axis : int, optional
Axis over which to compute the inverse FFT. If not given, the last axis is used.
 norm : {None, “ortho”}, optional
New in version 1.10.0.
Normalization mode (see
numpy.fft
). Default is None.
Returns:  out : ndarray
The truncated or zeropadded 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, or, if n is not given,
2*(m1)
wherem
is the length of the transformed axis of the input. To get an odd number of output points, n must be specified.
Raises:  IndexError
If axis is larger than the last axis of a.
See also
Notes
Returns the real valued npoint inverse discrete Fourier transform of a, where a contains the nonnegative frequency terms of a Hermitiansymmetric sequence. n is the length of the result, not the input.
If you specify an n such that a must be zeropadded 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
>>> 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 callingirfft
, the negative frequencies are not specified, and the output array is purely real.