nlcpy.fft.fft2

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

Computes 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

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 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. If s and axes have different length, or axes not given and len(s) != 2, ValueError occurs.
axessequence 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. If an element of axes is larger than than the number of axes of a, IndexError occurs.
norm{None, “ortho”},optional: Normalization mode. By default(None), the transforms are unscaled. It norm is set to “ortho”, the return values will be scaled by $1/\sqrt{n}$ .

Returns

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.

See also

ifft2: Computes the 2-dimensional inverse discrete fourier transform.
fft: Computes the one-dimensional discrete fourier transform.
fftn: Computes the n-dimensional discrete fourier transform.
fftshift: Shifts the zero-frequency component to the center of the spectrum.

Note

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.

Examples

>>> import nlcpy as vp
>>> import numpy as np
>>> a = np.mgrid[:5, :5][0]
>>> vp.fft.fft2(a)   
array([[ 50. +0.0000000000000000e+00j,   0. +0.0000000000000000e+00j, # may vary
          0. +0.0000000000000000e+00j,   0. +0.0000000000000000e+00j,
          0. +0.0000000000000000e+00j],
       [-12.5+1.7204774005889668e+01j,   0. +8.8817841970012523e-16j,
          0. +8.8817841970012523e-16j,   0. +8.8817841970012523e-16j,
          0. +8.8817841970012523e-16j],
       [-12.5+4.0614962029113286e+00j,   0. -2.2204460492503131e-16j,
          0. -2.2204460492503131e-16j,   0. -2.2204460492503131e-16j,
          0. -2.2204460492503131e-16j],
       [-12.5-4.0614962029113286e+00j,   0. +2.2204460492503131e-16j,
          0. +2.2204460492503131e-16j,   0. +2.2204460492503131e-16j,
          0. +2.2204460492503131e-16j],
       [-12.5-1.7204774005889668e+01j,   0. -8.8817841970012523e-16j,
          0. -8.8817841970012523e-16j,   0. -8.8817841970012523e-16j,
          0. -8.8817841970012523e-16j]])