Safe Haskell	None
Language	Haskell2010

Numeric.FFT

Description

Mixed-radix FFT calculation.

Arbitrary input vector lengths are handled using a mixed-radix Cooley-Tukey decimation in time algorithm with residual prime length vectors being treated using Rader's algorithm or hand-coded codelets for small primes.

Synopsis

Documentation

fft :: Vector v (Complex Double) => v (Complex Double) -> IO (v (Complex Double)) Source

Forward FFT with embedded plan calculation. For an input vector h of length N, with entries numbered from 0 to N - 1, calculates the entries in H, the discrete Fourier transform of h, as:

ifft :: Vector v (Complex Double) => v (Complex Double) -> IO (v (Complex Double)) Source

Inverse FFT with embedded plan calculation. For an input vector H of length N, with entries numbered from 0 to N - 1, representing Fourier amplitudes of a signal, calculates the entries in h, the inverse discrete Fourier transform of H, as:

fftWith :: Vector v (Complex Double) => Plan -> v (Complex Double) -> v (Complex Double) Source

Forward FFT with pre-computed plan.

ifftWith :: Vector v (Complex Double) => Plan -> v (Complex Double) -> v (Complex Double) Source

Inverse FFT with pre-computed plan.

plan :: Int -> IO Plan Source

Plan calculation for a given problem size.

planFromFactors :: Int -> (Int, Vector Int) -> IO Plan Source

Plan calculation for a given problem factorisation.

execute :: Plan -> Direction -> VCD -> VCD Source

Main FFT plan execution driver.

data Plan Source

A FFT plan. This depends only on the problem size and can be pre-computed and reused to transform (and inverse transform) any number of vectors of the given size.

Constructors

Plan

Fields

plDLInfo :: Vector (Int, Int, VVVCD, VVVCD): Size information and diagonal matrix entries for Danielson-Lanczos recursive decomposition of problem size.
plPermute :: Maybe VI: Input vector permutation to use before base transformation and recursive Danielson-Lanczos composition.
plBase :: BaseTransform: Base transformation used for each sub-vector before performing recursive Danielson-Lanczos steps to form the full FFT result.

Instances

Eq Plan
Show Plan

data Direction Source

Transform direction: Forward is the normal FFT, Inverse is inverse FFT.

Constructors

Forward
Inverse

Instances

Eq Direction
Show Direction

data BaseTransform Source

A "base transform" used at the "bottom" of the recursive Cooley-Tukey decomposition of the input problem size: either a simple DFT, a special hard-coded small problem size case, or a Rader prime-length FFT invocation.

Constructors

SpecialBase	Hard-coded small-size base transform.
Fields baseSize :: Int
DFTBase	Simple DFT base transform, giving problem size and powers of roots of unity needed for transform.
Fields baseSize :: Int dftWsFwd :: VCD dftWsInv :: VCD
RaderBase	Prime-length Rader FFT base transform, giving problem size, output index permutation (the input index permutation is folded into the main input permutation of the full transform), pre-transformed Rader b sequence for forward and inverse problems, the (padded or not) problem size for Rader sequence convolution and a sub-plan (either of size baseSize-1 or the next larger power of two) for computing the Rader convolution.
Fields baseSize :: Int raderOutPerm :: VI raderBFwd :: VCD raderBInv :: VCD raderConvSize :: Int raderConvPlan :: Plan

Instances

Eq BaseTransform
Show BaseTransform