----------------------------------------------------------------------------- -- | -- Module : Numeric.Transform.Fourier.SRDIF -- Copyright : (c) Matthew Donadio 2003 -- License : GPL -- -- Maintainer : m.p.donadio@ieee.org -- Stability : experimental -- Portability : portable -- -- Split-Radix Decimation in Frequency FFT -- ----------------------------------------------------------------------------- module Numeric.Transform.Fourier.SRDIF (fft_srdif) where import DSP.Basic (interleave) import Data.Array import Data.Complex ------------------------------------------------------------------------------- -- | Split-Radix Decimation in Frequency FFT {-# specialize fft_srdif :: Array Int (Complex Float) -> Int -> (Array Int (Complex Float) -> Array Int (Complex Float)) -> Array Int (Complex Float) #-} {-# specialize fft_srdif :: Array Int (Complex Double) -> Int -> (Array Int (Complex Double) -> Array Int (Complex Double)) -> Array Int (Complex Double) #-} fft_srdif :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) -- ^ x[n] -> a -- ^ N -> (Array a (Complex b) -> Array a (Complex b)) -- ^ FFT function -> Array a (Complex b) -- ^ X[k] fft_srdif x n fft = listArray (0,n-1) \$ c where c2k = elems \$ fft \$ listArray (0,n2-1) x2k c4k1 = elems \$ fft \$ listArray (0,n4-1) x4k1 c4k3 = elems \$ fft \$ listArray (0,n4-1) x4k3 c = interleave c2k \$ interleave c4k1 c4k3 x2k = [ x!i + x!(i+n2) | i <- [0..n2-1] ] x4k1 = [ (x!i - x!(i+n2) - j * (x!(i+n4) - x!(i+n34))) * w!i | i <- [0..n4-1] ] x4k3 = [ (x!i - x!(i+n2) + j * (x!(i+n4) - x!(i+n34))) * w!(3*i) | i <- [0..n4-1] ] j = 0 :+ 1 wn = cis (-2 * pi / fromIntegral n) w = listArray (0,n-1) \$ iterate (* wn) 1 n2 = n `div` 2 n4 = n `div` 4 n34 = 3 * n4