Spectrum.hs

module Spectrum ( computeSpectrum
                , sumSpectrum
                ) where

import Data.Complex

{- 
  N samples
  R sample rate
  
  So frequency spacing is R / N
-}

-- http://stackoverflow.com/questions/604453/analyze-audio-using-fast-fourier-transform?rq=1

computeSpectrum :: [Complex Double] -> Double -> [(Double, Double)]
computeSpectrum input sampleRate = normalize(zip frequencies (magnitudes input))
  where frequencies = [i * resolution | i <- [0..(halfNumSamples - 1)]]
        endBound = (numSamples - 1)
        ratio = (numSamples + 1) / sampleRate
        resolution = 1 / ratio
        numSamples = fromIntegral(length input)
        halfNumSamples = numSamples / 2

normalize :: [(Double, Double)] -> [(Double, Double)]
normalize complexes = map (\(f, x) -> (f, 10 * (logBase 10 (x + 1e-20)))) complexes


sumSpectrum :: [Complex Double] -> Double -> Double
sumSpectrum input sampleRate = sum firsts
  where firsts = map fst $ computeSpectrum input sampleRate


magnitudes zs = map Data.Complex.magnitude zs