flopscope.

flopscope.numpy.fft.fft2

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

Compute the 2-dimensional discrete Fourier Transform.

Adapted from NumPy docs np.fft.fft2

Areafft
Typecustom
NumPy Refnp.fft.fft2
Cost
5N⋅⌈log⁡2N⌉5N \cdot \lceil\log_2 N\rceil
Flopscope Context

2-D complex FFT. Cost: 5*N*ceil(log2(N)), N=prod(s) (Cooley-Tukey radix-2; Van Loan 1992 §1.4).

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[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.

Changed in version 2.0.

If s is not given, the shape of the input along the axes specified by axes is used.

Deprecated since 2.0.
Deprecated since 2.0.
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. Default: (-2, -1).

Deprecated since 2.0.
norm:{"backward", "ortho", "forward"}, optional

Normalization mode (see flops.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

Added in version 1.20.0.
out:complex ndarray, optional

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

Added in version 2.0.0.

Returns

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.

Raises

: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.

See also

  • flops.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 flops.fft for definitions and conventions used.

Examples

>>> import flopscope.numpy as fnp
>>> a = flops.mgrid[:5, :5][0]
>>> flops.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        ]])