Here is a small Python implementation of the Fourier transform via Pade approximants found in this paper

Bruner, Adam, Daniel LaMaster, and Kenneth Lopata. "Accelerated broadband spectra using transition dipole decomposition and Padé approximants." Journal of chemical theory and computation 12.8 (2016): 3741-3750.

Installation

pip install -r requirements.txt
pip install -e .

Example

Usage is very simple. Here is an example:

First, let's make a time series

import numpy as np
from pade import pade

w  = 2.0
dt = 0.02
N  = 5000
t  = np.linspace(0,dt*N, N, endpoint=False)
signal = np.sin(2*t) + np.sin(4*t) + np.sin(8*t)

Which looks like this

Then we do the Pade

fw, frequency = pade(t,signal)

which, when we plot the imaginary component, looks like this

Which is what we expect, since our sinusoidal signal had frequencies at 2, 4 and 8. Note the agreement between FFT implementation from SciPy overlaid in the above figure.

You can look at the arguments in pade.py for more options, most relating to what frequencies you ultimately want to evaluate the transformed signal over. (The Pade-approximant method actually yields a rational function, so it's up to the user to choose the domain.)