fft¶

powerbox.dft.fft(X, L=None, Lk=None, a=0, b=6.283185307179586, axes=None, ret_cubegrid=False)[source]¶

Arbitrary-dimension nice Fourier Transform.

This function wraps numpy’s fftn and applies some nice properties. Notably, the returned fourier transform is equivalent to what would be expected from a continuous Fourier Transform (including normalisations etc.). In addition, arbitrary conventions are supported (see powerbox.dft for details).

Default parameters have the same normalising conventions as numpy.fft.fftn.

The output object always has the zero in the centre, with monotonically increasing spectral arguments.

Parameters:

X : array: An array with arbitrary dimensions defining the field to be transformed. Should correspond exactly to the continuous function for which it is an analogue. A lower-dimensional transform can be specified by using the axes argument.
L : float or array-like, optional: The length of the box which defines X. If a scalar, each transformed dimension in X is assumed to have the same length. If array-like, must be of the same length as the number of transformed dimensions. The default returns the un-normalised DFT (same as numpy).
Lk : float or array-like, optional: The length of the fourier-space box which defines the dual of X. Only one of L/Lk needs to be provided. If provided, L takes precedence. If a scalar, each transformed dimension in X is assumed to have the same length. If array-like, must be of the same length as the number of transformed dimensions.
a,b : float, optional: These define the Fourier convention used. See powerbox.dft for details. The defaults return the standard DFT as defined in numpy.fft.
axes : sequence of ints, optional: The axes to take the transform over. The default is to use all axes for the transform.
ret_cubegrid : bool, optional: Whether to return the entire grid of frequency magnitudes.

Returns:

ft : array: The DFT of X, normalised to be consistent with the continuous transform.
freq : list of arrays: The frequencies in each dimension, consistent with the Fourier conventions specified.
grid : array: Only returned if ret_cubegrid is True. An array with shape given by axes specifying the magnitude of the frequencies at each point of the fourier transform.