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 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 
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

irfftn
 The inverse of
rfftn
, i.e. the inverse of the ndimensional FFT of real input. 
fft
 The onedimensional FFT, with definitions and conventions used.

rfft
 The onedimensional FFT of real input.

fftn
 The ndimensional FFT.

rfft2
 The twodimensional 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
>>> a = np.ones((2, 2, 2))
>>> np.fft.rfftn(a)
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]]])
>>> np.fft.rfftn(a, 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]]])