scipy.fft.rfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *, plan=None)[source]#

Compute the N-D discrete Fourier Transform for real input.

This function computes the N-D discrete Fourier Transform over any number of axes in an M-D 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.


Input array, taken to be real.

ssequence 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 for rfft(x, n), while for the remaining axes, it corresponds to n for fft(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.

axessequence 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{“backward”, “ortho”, “forward”}, optional

Normalization mode (see fft). Default is “backward”.

overwrite_xbool, optional

If True, the contents of x can be destroyed; the default is False. See fft for more details.

workersint, optional

Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count(). See fft for more details.

planobject, optional

This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

Added in version 1.5.0.

outcomplex ndarray

The truncated or zero-padded input, transformed along the axes indicated by axes, or by a combination of s and x, 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.


If s and axes have different length.


If an element of axes is larger than the number of axes of x.

See also


The inverse of rfftn, i.e., the inverse of the N-D FFT of real input.


The 1-D FFT, with definitions and conventions used.


The 1-D FFT of real input.


The N-D FFT.


The 2-D FFT of real input.


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 by fftn. The order of the output is as for rfft for the final transformation axis, and as for fftn for the remaining transformation axes.

See fft for details, definitions and conventions used.


>>> import scipy.fft
>>> import numpy as np
>>> x = np.ones((2, 2, 2))
>>> scipy.fft.rfftn(x)
array([[[8.+0.j,  0.+0.j], # may vary
        [0.+0.j,  0.+0.j]],
       [[0.+0.j,  0.+0.j],
        [0.+0.j,  0.+0.j]]])
>>> scipy.fft.rfftn(x, axes=(2, 0))
array([[[4.+0.j,  0.+0.j], # may vary
        [4.+0.j,  0.+0.j]],
       [[0.+0.j,  0.+0.j],
        [0.+0.j,  0.+0.j]]])