flexft 0.1.0

Flexible-grid approximations to continuous Fourier transforms

FlexFT

FlexFT evaluates finite-sum approximations to continuous Fourier transforms on uniform input and output grids whose spacings can be chosen independently. It uses the Bailey--Swarztrauber fractional DFT/Bluestein convolution, implemented with JAX FFTs.

For samples on

x[n] = x0 + (n - floor(N / 2)) * dx

the forward transform returns approximations on

k[m] = k0 + (m - floor(N / 2)) * dk.

Installation

pip install flexft

Quick start

import jax.numpy as jnp
from flexft import flexft, iflexft

N = 256
dx = 0.05
dk = 0.02
x = (jnp.arange(N) - N // 2) * dx
f = jnp.exp(-(x**2))

F = flexft(f, dx=dx, dk=dk)
f_inverse_approximation = iflexft(F, dk=dk, dx=dx)

Omit dk in the forward transform to use the FFT-compatible spacing 1 / (N * dx). Conversely, omit dx in the inverse transform to use 1 / (N * dk).

For repeated transforms with unchanged grids, construct and reuse FlexFT or IFlexFT; this reuses the precomputed convolution kernel.

See the documentation for the derivation, shifted grids, 2D transforms, and more examples.