irfft(a, n=None, axis=-1, norm=None)¶
Compute the inverse of the n-point DFT for real input.
This function computes the inverse of the one-dimensional n-point
discrete Fourier Transform of real input computed by
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.
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
m is the length of the input along the axis
specified by axis.
Axis over which to compute the inverse FFT. If not given, the last axis is used.
New in version 1.10.0.
Normalization mode (see
numpy.fft). Default is None.
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, or, if n is not given,
m is the length of the transformed axis of the
input. To get an odd number of output points, n must be specified.
If axis is larger than the last axis of a.
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,
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.
>>> 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.