haskell-fft

Straight-forward implementation of 1-D Fast Fourier Transform (FFT), its inverse, and Welch Power Spectral Density (PSD) estimation in Haskell. Implements the Cooley-Tukey FFT algorithm for real and complex timeseries data. Variants of the following numpy functions are implemented:

• numpy.fft.fft
• numpy.fft.ifft
• numpy.fft.rfft
• numpy.fft.irfft
• numpy.fft.fftfreq
• scipy.signal.hann
• scipy.signal.welch

Requirements

Haskell Stack

Installation

stack install
stack test

Example Usage

FFT (and inverse) of real-valued timeseries:

import FFT

fourier_components = rfft [1..10]
frequencies = fftfreq 10 1
timeseries = irfft fourier_components

FFT (and inverse) of complex-valued timeseries:

import FFT
import Data.Complex

fourier_components = fft [mkPolar i (pi/i) | i <- [1..10]]
frequencies = fftfreq 10 1
timeseries = ifft fourier_components

Welch Power Spectral Density (PSD) estimation:

import Signal
(frequencies, psd) = welch [1..100] 10 2