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 tonforfft(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 not
None,axes must not beNoneeither.Deprecated since version 2.0:s must contain only
ints, notNonevalues.Nonevalues currently mean that the default value fornis 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 be
None.- norm{“backward”, “ortho”, “forward”}, optional
Normalization mode (see
numpy.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 have
snot 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 and
len(s)!=2.- IndexError
If an element ofaxes is larger than than the number of axes ofa.
See also
numpy.fftOverall view of discrete Fourier transforms, with definitions and conventions used.
ifft2The inverse two-dimensional FFT.
fftThe one-dimensional FFT.
fftnThen-dimensional FFT.
fftshiftShifts zero-frequency terms to the center of the array. For two-dimensional input, swaps first and third quadrants, and second and fourth quadrants.
Notes
fft2is justfftnwith a different default foraxes.The output, analogously to
fft, 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.See
fftnfor details and a plotting example, andnumpy.fftfordefinitions 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 ]])