numpy.fft.rfftn¶

numpy.fft.
rfftn
(a, s=None, axes=None, norm=None)[source]¶ Compute the Ndimensional discrete Fourier Transform for real input.
This function computes the Ndimensional discrete Fourier Transform over any number of axes in an Mdimensional real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex.
Parameters: a : array_like
Input array, taken to be real.
s : sequence of ints, optional
Shape (length along each transformed axis) to use from the input. (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). The final element of s corresponds to n forrfft(x, n)
, while for the remaining axes, it corresponds to n forfft(x, n)
. Along any axis, if the given shape 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.axes : sequence of ints, optional
Axes over which to compute the FFT. If not given, the last
len(s)
axes are used, or all axes if s is also not specified.norm : {None, “ortho”}, optional
New in version 1.10.0.
Normalization mode (see
numpy.fft
). Default is None.Returns: out : complex ndarray
The truncated or zeropadded input, transformed along the axes indicated by axes, or by a combination of s and a, as explained in the parameters section above. The length of the last axis transformed will be
s[1]//2+1
, while the remaining transformed axes will have lengths according to s, or unchanged from the input.Raises: ValueError
If s and axes have different length.
IndexError
If an element of axes is larger than than the number of axes of a.
See also
Notes
The transform for real input is performed over the last transformation axis, as by
rfft
, then the transform over the remaining axes is performed as byfftn
. The order of the output is as forrfft
for the final transformation axis, and as forfftn
for the remaining transformation axes.See
fft
for details, definitions and conventions used.Examples
>>> a = np.ones((2, 2, 2)) >>> np.fft.rfftn(a) array([[[ 8.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]], [[ 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]]])
>>> np.fft.rfftn(a, axes=(2, 0)) array([[[ 4.+0.j, 0.+0.j], [ 4.+0.j, 0.+0.j]], [[ 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]]])