/NumPy 1.17

# numpy.fft.fft2

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

Compute the 2-dimensional discrete Fourier Transform

This function computes the n-dimensional discrete Fourier Transform over any axes in an M-dimensional 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.

Parameters: `a : array_like` Input array, can be complex `s : sequence of ints, optional` Shape (length of each transformed axis) of the output (`s` refers to axis 0, `s` 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, optional` Axes over which to compute the FFT. If not given, the last two axes are used. A repeated index in `axes` means the transform over that axis is performed multiple times. A one-element sequence means that a one-dimensional FFT is performed. `norm : {None, “ortho”}, optional` New in version 1.10.0. Normalization mode (see `numpy.fft`). Default is None. `out : complex ndarray` The truncated or zero-padded input, transformed along the axes indicated by `axes`, or the last two axes if `axes` is not given. ValueError If `s` and `axes` have different length, or `axes` not given and `len(s) != 2`. IndexError If an element of `axes` is larger than than the number of axes of `a`.

`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`
The n-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 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 `numpy.fft` for definitions and conventions used.

#### Examples

```>>> a = np.mgrid[:5, :5]
>>> 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        ]])
```