irfftn(a, s=None, axes=None, norm=None)¶
Compute the inverse of the N-dimensional FFT of real input.
This function computes the inverse of the N-dimensional discrete
Fourier Transform for real input over any number of axes in an
M-dimensional array by means of the Fast Fourier Transform (FFT). In
irfftn(rfftn(a), a.shape) == a to within numerical
a.shape is necessary like
len(a) is for
and for the same reason.)
Shape (length of each transformed axis) of the output
s refers to axis 0,
s to axis 1, etc.). s is also the
number of input points used along this axis, except for the last axis,
s[-1]//2+1 points of the input are used.
Along any axis, if the shape indicated by s is smaller than that of
the input, the input is cropped. If it is larger, the input is padded
with zeros. If s is not given, the shape of the input along the axes
specified by axes is used. Except for the last axis which is taken to be
m is the length of the input along that axis.
Axes over which to compute the inverse FFT. If not given, the last len(s) axes are used, or all axes if s is also not specified. Repeated indices in axes means that the inverse transform over that axis is performed multiple times.
New in version 1.10.0.
Normalization mode (see
numpy.fft). Default is None.
The truncated or zero-padded input, transformed along the axes
indicated by axes, or by a combination of s or a,
as explained in the parameters section above.
The length of each transformed axis is as given by the corresponding
element of s, or the length of the input in every axis except for the
last one if s is not given. In the final transformed axis the length
of the output when s is not given is
m is the
length of the final transformed axis of the input. To get an odd
number of output points in the final axis, s must be specified.
If s and axes have different length.
If an element of axes is larger than than the number of axes of a.
fft for definitions and conventions used.
rfft for definitions and conventions used for real input.
The correct interpretation of the hermitian input depends on the shape of
the original data, as given by s. 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. When performing the
final complex to real transform, the last value is thus treated as purely
real. To avoid losing information, the correct shape of the real input
must be given.
>>> a = np.zeros((3, 2, 2)) >>> a[0, 0, 0] = 3 * 2 * 2 >>> np.fft.irfftn(a) array([[[1., 1.], [1., 1.]], [[1., 1.], [1., 1.]], [[1., 1.], [1., 1.]]])