fft.fftn

Description

Compute the N-dimensional discrete Fourier Transform.

Mandatory Input Parameters

Parameter	Type	Description
a	array_like	Input array, which can be a complex number

Optional Input Parameters

Parameter	Type	Default Value	Description
s	sequence of ints	None	Output shape (length of each transformed axis. s[0] refers to axis 0, s[1] to axis 1, etc.). This corresponds to n for fft(x, n). Along each 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	-1	Axis over which to compute the FFT. If not given, the last n axes are used.
norm	{"backward", "ortho", "forward"}, optional	backward	Normalization mode (see numpy.fft). It indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

Parameter

Type

Default Value

Description

sequence of ints

None

Output shape (length of each transformed axis. s[0] refers to axis 0, s[1] to axis 1, etc.). This corresponds to n for fft(x, n). Along each 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

-1

Axis over which to compute the FFT. If not given, the last n axes are used.

norm

{"backward", "ortho", "forward"}, optional

backward

Normalization mode (see numpy.fft). It indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

Return Value

Type	Description
ndarray	The truncated or zero-padded input, transformed along the axes specified by axes, or the last n axes if axes is not specified.

Examples

>>> import numpy as np
>>> a = np.mgrid[:3, :3, :3][0]
>>> a
array([[[0, 0, 0],
        [0, 0, 0],
        [0, 0, 0]],

       [[1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]],

       [[2, 2, 2],
        [2, 2, 2],
        [2, 2, 2]]])
>>> 
>>> np.fft.fftn(a)
array([[[ 27. +0.j        ,   0. +0.j        ,   0. +0.j        ],
        [  0. +0.j        ,   0. +0.j        ,   0. +0.j        ],
        [  0. +0.j        ,   0. +0.j        ,   0. +0.j        ]],

       [[-13.5+7.79422863j,   0. +0.j        ,   0. +0.j        ],
        [  0. +0.j        ,   0. +0.j        ,   0. +0.j        ],
        [  0. +0.j        ,   0. +0.j        ,   0. +0.j        ]],

       [[-13.5-7.79422863j,   0. +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.fftn(a, (2,2), axes=(0,1))
array([[[ 2.+0.j,  2.+0.j,  2.+0.j],
        [ 0.+0.j,  0.+0.j,  0.+0.j]],

       [[-2.+0.j, -2.+0.j, -2.+0.j],
        [ 0.+0.j,  0.+0.j,  0.+0.j]]])
>>>

Parent topic: Fourier Transform Functions