SciPy

scipy.fft.rfftn

scipy.fft.rfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=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.

Parameters
xarray_like

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{None, “ortho”}, optional

Normalization mode (see fft). Default is None.

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.

Returns
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.

Raises
ValueError

If s and axes have different length.

IndexError

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

See also

irfftn

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

fft

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

rfft

The 1-D FFT of real input.

fftn

The N-D FFT.

rfft2

The 2-D FFT of real input.

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 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.

Examples

>>> import scipy.fft
>>> 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]]])

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