scipy.fft.fft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *, plan=None)[source]#

Compute the 2-D discrete Fourier Transform

This function computes the N-D discrete Fourier Transform over any axes in an M-D array by means of the Fast Fourier Transform (FFT). By default, the transform is computed over the last two axes of the input array, i.e., a 2-dimensional FFT.


Input array, can be complex

ssequence of ints, optional

Shape (length of each transformed axis) of the output (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.

axessequence of ints, optional

Axes over which to compute the FFT. If not given, the last two axes are used.

norm{“backward”, “ortho”, “forward”}, optional

Normalization mode (see fft). Default is “backward”.

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.

planobject, optional

This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

Added in version 1.5.0.

outcomplex ndarray

The truncated or zero-padded input, transformed along the axes indicated by axes, or the last two axes if axes is not given.


If s and axes have different length, or axes not given and len(s) != 2.


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

See also


The inverse 2-D FFT.


The 1-D FFT.


The N-D FFT.


Shifts zero-frequency terms to the center of the array. For 2-D input, swaps first and third quadrants, and second and fourth quadrants.


fft2 is just fftn with a different default for axes.

The output, analogously to fft, contains the term for zero frequency in the low-order corner of the transformed axes, the positive frequency terms in the first half of these axes, the term for the Nyquist frequency in the middle of the axes and the negative frequency terms in the second half of the axes, in order of decreasingly negative frequency.

See fftn for details and a plotting example, and fft for definitions and conventions used.


>>> import scipy.fft
>>> import numpy as np
>>> x = np.mgrid[:5, :5][0]
>>> scipy.fft.fft2(x)
array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        , # may vary
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ]])