----------------------------------------------------------------------------- -- | -- Module : Numeric.Random.Spectrum.Pink -- Copyright : (c) Matthew Donadio 2003 -- License : GPL -- -- Maintainer : m.p.donadio@ieee.org -- Stability : experimental -- Portability : portable -- -- Functions for pinking noise -- -- -- ----------------------------------------------------------------------------- module Numeric.Random.Spectrum.Pink (kellet, voss) where import DSP.Basic (downsample, upsampleAndHold) import Data.List (tails) ------------------------------------------------------------------------------- -- rb-j filter -- pole zero -- ---- ---- -- 0.99572754 0.98443604 -- 0.94790649 0.83392334 -- 0.53567505 0.07568359 ------------------------------------------------------------------------------- -- | Kellet's filter -- b0 = 0.99886 * b0 + white * 0.0555179; -- b1 = 0.99332 * b1 + white * 0.0750759; -- b2 = 0.96900 * b2 + white * 0.1538520; -- b3 = 0.86650 * b3 + white * 0.3104856; -- b4 = 0.55000 * b4 + white * 0.5329522; -- b5 = -0.7616 * b5 - white * 0.0168980; -- pink = b0 + b1 + b2 + b3 + b4 + b5 + b6 + white * 0.5362; -- b6 = white * 0.115926; kellet :: [Double] -- ^ noise -> [Double] -- ^ pinked noise kellet w = kellet' w 0 0 0 0 0 0 0 where kellet' [] _ _ _ _ _ _ _ = [] kellet' (white:ws) b0 b1 b2 b3 b4 b5 b6 = pink : kellet' ws b0' b1' b2' b3' b4' b5' b6' where b0' = 0.99886 * b0 + white * 0.0555179 b1' = 0.99332 * b1 + white * 0.0750759 b2' = 0.96900 * b2 + white * 0.1538520 b3' = 0.86650 * b3 + white * 0.3104856 b4' = 0.55000 * b4 + white * 0.5329522 b5' = -0.7616 * b5 - white * 0.0168980 pink = b0 + b1 + b2 + b3 + b4 + b5 + b6 + white * 0.5362 b6' = white * 0.115926 ------------------------------------------------------------------------------- -- voss algorithm add :: Num a => [[a]] -> [a] add = foldl1 (zipWith (+)) split :: Int -> [a] -> [[a]] split n = take n . map (downsample n) . (++repeat []) . tails mkOctaves :: [[a]] -> [[a]] mkOctaves = mkOctaves' 1 where mkOctaves' _ [] = [] mkOctaves' n (xs:xss) = upsampleAndHold n xs : mkOctaves' (2*n) xss -- | Voss's algorithm -- -- UNTESTED, but the algorithm looks like it is working based on my hand -- tests. -- TODO: Since the input noise is consumed in different speed for the octaves -- the function will certainly leak memory. voss :: Int -- ^ number of octaves to sum -> [Double] -- ^ noise -> [Double] -- ^ pinked noise voss n w = add $ mkOctaves $ split n w ------------------------------------------------------------------------------- -- voss-mccartney algorithm ------------------------------------------------------------------------------- -- vm w =