scipy.fftpack.fftn

scipy.fftpack.fftn(x, shape=None, axes=None, overwrite_x=0)

fftn(x, shape=None, axes=None, overwrite_x=0) -> y

Return multi-dimensional discrete Fourier transform of arbitrary type sequence x.

The returned array contains

y[j_1,..,j_d] = sum[k_1=0..n_1-1, ..., k_d=0..n_d-1]

x[k_1,..,k_d] * prod[i=1..d] exp(-sqrt(-1)*2*pi/n_i * j_i * k_i)

where d = len(x.shape) and n = x.shape. Note that y[..., -j_i, ...] = y[..., n_i-j_i, ...].conjugate().

Optional input:

shape

Defines the shape of the Fourier transform. If shape is not specified then shape=take(x.shape,axes,axis=0). If shape[i]>x.shape[i] then the i-th dimension is padded with zeros. If shape[i]<x.shape[i], then the i-th dimension is truncated to desired length shape[i].

axes

The transform is applied along the given axes of the input array (or the newly constructed array if shape argument was used).

overwrite_x

If set to true, the contents of x can be destroyed.

Notes:

y == fftn(ifftn(y)) within numerical accuracy.