powerbox.dft Module

A module defining some “nicer” fourier transform functions.

We define only two functions – an arbitrary-dimension forward transform, and its inverse. In each case, the transform is designed to replicate the continuous transform. That is, the transform is volume-normalised and obeys correct Fourier conventions.

The actual FFT backend is provided by pyFFTW if it is installed, which provides a significant speedup, and multi-threading.

Conveniently, we allow for arbitrary Fourier convention, according to the scheme in http://mathworld.wolfram.com/FourierTransform.html. That is, we define the forward and inverse n-dimensional transforms respectively as

\[F(k) = \sqrt{\frac{|b|}{(2\pi)^{1-a}}}^n \int f(r) e^{-i b\mathbf{k}\cdot\mathbf{r}} d^n\mathbf{r}\]

and

\[f(r) = \sqrt{\frac{|b|}{(2\pi)^{1+a}}}^n \int F(k) e^{+i b\mathbf{k}\cdot\mathbf{r}} d^n \mathbf{k}.\]

In both transforms, the corresponding co-ordinates are returned so a completely consistent transform is simple to get. This makes switching from standard frequency to angular frequency very simple.

We note that currently, only positive values for b are implemented (in fact, using negative b is consistent, but one must be careful that the frequencies returned are descending, rather than ascending).

Functions

fft(X[, L, Lk, a, b, axes, ret_cubegrid])	Arbitrary-dimension nice Fourier Transform.
ifft(X[, Lk, L, a, b, axes, ret_cubegrid])	Arbitrary-dimension nice inverse Fourier Transform.
fftfreq(N[, d, b])	Return the fourier frequencies for a box with N cells, using general Fourier convention.
fftshift(x, *args, **kwargs)	The same as numpy’s fftshift, except that it preserves units (if Astropy quantities are used)
ifftshift(x, *args, **kwargs)	The same as numpy’s ifftshift, except that it preserves units (if Astropy quantities are used)