hommage-0.0.5: Haskell Offline Music Manipulation And Generation EDSL Source code Contents Index

Sound.Hommage.FFT

Contents FFT FFT

Description

This module implements the Fast Fourier Transformation purely in Haskell.

Synopsis

fft :: Int -> [Double] -> [[Complex Double]] fft' :: Int -> [Complex Double] -> [Double] fftt :: Int -> ([[Complex Double]] -> [Complex Double]) -> [Double] -> [Double] fftc :: Int -> [Complex Double] -> [[Complex Double]] fftc' :: Int -> [Complex Double] -> [[Complex Double]] ffttv :: Int -> [Double] -> [Double] -> [Double] fftco :: Int -> [Complex Double] -> [[Complex Double]] fftco' :: Int -> [Complex Double] -> [Complex Double] rect_transform :: Floating a => Int -> [a] -> [[a]] rect_filter :: Floating a => Int -> ([[a]] -> [[a]]) -> [a] -> [a] rect_filter' :: Floating a => Int -> [[a]] -> [a] -> [a] i :: Complex Double w :: Int -> Complex Double ws :: Bool -> Int -> [Complex Double] map2 :: (a -> a -> b) -> [a] -> [b] zip2 :: [a] -> [a] -> [a] evens odds drop_odds appendpair :: ([a], [a]) -> [a] reorder :: Int -> [[a]] -> [[a]] reorder_init reorder_init' :: [a] -> [[a]] butterfly :: Complex Double -> Complex Double -> Complex Double -> (Complex Double, Complex Double) butterfly' :: Complex Double -> Complex Double -> Complex Double -> (Complex Double, Complex Double) fft_level :: [Complex Double] -> [[Complex Double]] -> [[Complex Double]] fft_merge :: [Complex Double] -> [Complex Double] -> [Complex Double] -> ([Complex Double], [Complex Double]) fft_init_overlap fft_level' :: [Complex Double] -> [[Complex Double]] -> [[Complex Double]] fft_merge' :: [Complex Double] -> [Complex Double] -> [Complex Double] -> ([Complex Double], [Complex Double]) fft_init fft_overlap_loop expandComplex overlap_curve :: Int -> [Double] mix_overlap :: Int -> [[Double]] -> [Double]

FFT

fft :: Int -> [Double] -> [[Complex Double]] Source

FFT transformation. Input is grouped into overlapping parts of 2^(N+2) reals and mapped to sublists with 2^(N+1) complex numbers.

fft' :: Int -> [Complex Double] -> [Double] Source

Inverse FFT transformation. Complex input is grouped into parts with length 2^(N+1) and mapped to sublists with 2^(N+2) reals, which are overlapped and mixed.

fftt :: Int -> ([[Complex Double]] -> [Complex Double]) -> [Double] -> [Double] Source

FFT transformation with overlapping and windowing. Argument function maps the coefficients. Windowsize: 2^(N+2), i. e. 2^(N+1) coefficients

FFT

fftc :: Int -> [Complex Double] -> [[Complex Double]] Source

FFT transformation for complex input (segments of length 2^n). No overlapping or windowing.

fftc' :: Int -> [Complex Double] -> [[Complex Double]] Source

Inverse FFT transformation for complex input (segments of length 2^n). No overlapping or windowing.

ffttv :: Int -> [Double] -> [Double] -> [Double] Source

fftco :: Int -> [Complex Double] -> [[Complex Double]] Source

FFT for complex input with overlapping. Segment-size: 2^(n+1)

fftco' :: Int -> [Complex Double] -> [Complex Double] Source

rect_transform :: Floating a => Int -> [a] -> [[a]] Source

A self-inverse transformation similar to FFT but with a simple butterfly operation that uses always W=1. Modifying the data between application and inverse is similar to filtering but the result will be built up from rectangle waves instead of sinus waves.

rect_filter :: Floating a => Int -> ([[a]] -> [[a]]) -> [a] -> [a] Source

rect_filter' :: Floating a => Int -> [[a]] -> [a] -> [a] Source

i :: Complex Double Source

The complex value i = (0 :+ 1)

w :: Int -> Complex Double Source

The n-th root of 1

ws :: Bool -> Int -> [Complex Double] Source

the 2n-th root with exponents 0, 1, .. n. False=inverse (exponents are negated)

map2 :: (a -> a -> b) -> [a] -> [b] Source

zip2 :: [a] -> [a] -> [a] Source

evens

odds

drop_odds

appendpair :: ([a], [a]) -> [a] Source

returns [] if argument has zero or one element.

reorder :: Int -> [[a]] -> [[a]] Source

list is grouped into sublists with length N (must be power of 2) and bitwise reverse order

reorder_init

reorder_init' :: [a] -> [[a]] Source

butterfly :: Complex Double -> Complex Double -> Complex Double -> (Complex Double, Complex Double) Source

butterfly' :: Complex Double -> Complex Double -> Complex Double -> (Complex Double, Complex Double) Source

fft_level :: [Complex Double] -> [[Complex Double]] -> [[Complex Double]] Source

fft_merge :: [Complex Double] -> [Complex Double] -> [Complex Double] -> ([Complex Double], [Complex Double]) Source

fft_init_overlap

fft_level' :: [Complex Double] -> [[Complex Double]] -> [[Complex Double]] Source

fft_merge' :: [Complex Double] -> [Complex Double] -> [Complex Double] -> ([Complex Double], [Complex Double]) Source

fft_init

fft_overlap_loop

expandComplex

overlap_curve :: Int -> [Double] Source

Creates a fade with length N

mix_overlap :: Int -> [[Double]] -> [Double] Source

Overlaps a sequence of parts of length N (overlaps by N/2).

Produced by Haddock version 2.4.2