numpy.fft.fft2#

fft.fft2(a,s=None,axes=(-2,-1),norm=None,out=None)[source]#

Compute the 2-dimensional discrete Fourier Transform.

This function computes then-dimensional discrete Fourier Transformover any axes in anM-dimensional array by means of theFast Fourier Transform (FFT). By default, the transform is computed overthe last two axes of the input array, i.e., a 2-dimensional FFT.

Parameters:
aarray_like

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 ton forfft(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.

Changed in version 2.0:If it is-1, the whole input is used (no padding/trimming).

Ifs is not given, the shape of the input along the axes specifiedbyaxes is used.

Deprecated since version 2.0:Ifs is notNone,axes must not beNone either.

Deprecated since version 2.0:s must contain onlyint s, notNone values.Nonevalues currently mean that the default value forn is usedin the corresponding 1-D transform, but this behaviour isdeprecated.

axessequence of ints, optional

Axes over which to compute the FFT. If not given, the last twoaxes are used. A repeated index inaxes means the transform overthat axis is performed multiple times. A one-element sequence meansthat a one-dimensional FFT is performed. Default:(-2,-1).

Deprecated since version 2.0:Ifs is specified, the correspondingaxes to be transformedmust not beNone.

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

Normalization mode (seenumpy.fft). Default is “backward”.Indicates which direction of the forward/backward pair of transformsis scaled and with what normalization factor.

New in version 1.20.0:The “backward”, “forward” values were added.

outcomplex ndarray, optional

If provided, the result will be placed in this array. It should beof the appropriate shape and dtype for all axes (and hence only thelast axis can haves not equal to the shape at that axis).

New in version 2.0.0.

Returns:
outcomplex ndarray

The truncated or zero-padded input, transformed along the axesindicated byaxes, or the last two axes ifaxes is not given.

Raises:
ValueError

Ifs andaxes have different length, oraxes not given andlen(s)!=2.

IndexError

If an element ofaxes is larger than than the number of axes ofa.

See also

numpy.fft

Overall view of discrete Fourier transforms, with definitions and conventions used.

ifft2

The inverse two-dimensional FFT.

fft

The one-dimensional FFT.

fftn

Then-dimensional FFT.

fftshift

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

Notes

fft2 is justfftn with a different default foraxes.

The output, analogously tofft, contains the term for zero frequency inthe low-order corner of the transformed axes, the positive frequency termsin the first half of these axes, the term for the Nyquist frequency in themiddle of the axes and the negative frequency terms in the second half ofthe axes, in order of decreasingly negative frequency.

Seefftn for details and a plotting example, andnumpy.fft fordefinitions and conventions used.

Examples

>>>importnumpyasnp>>>a=np.mgrid[:5,:5][0]>>>np.fft.fft2(a)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        ]])
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