numpy.fft.rfftn(a, s=None, axes=None, norm=None)[source]

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

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


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 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.

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.


out : complex ndarray

The truncated or zero-padded 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.



If s and axes have different length.


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

See also

The inverse of rfftn, i.e. the inverse of the n-dimensional FFT of real input.
The one-dimensional FFT, with definitions and conventions used.
The one-dimensional FFT of real input.
The n-dimensional FFT.
The two-dimensional 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.


>>> 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]]])

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