-- This code was automatically generated by lhs2tex --code, from the file 
-- HSoM/SpectrumAnalysis.lhs.  (See HSoM/MakeCode.bat.)

{-# LANGUAGE Arrows #-}

module Euterpea.Music.Signal.SpectrumAnalysis where

import Euterpea
import Euterpea.Experimental (fftA)

import Data.Complex (Complex ((:+)), polar)
import Data.Maybe (listToMaybe, catMaybes)

dft :: RealFloat a => [Complex a] -> [Complex a]
dft xs = 
  let  lenI = length xs
       lenR = fromIntegral lenI
       lenC = lenR :+ 0
  in [  let i = -2 * pi * fromIntegral k / lenR
        in (1/lenC) * sum [  (xs!!n) * exp (0 :+ i * fromIntegral n)
                             | n <- [0,1..lenI-1] ]
        | k <- [0,1..lenI-1] ]
mkTerm :: Int -> Double -> [Complex Double]
mkTerm num n = let f = 2 * pi / fromIntegral num
               in [  sin (n * f * fromIntegral i) / n :+ 0
                     | i <- [0,1..num-1] ]

mkxa, mkxb, mkxc :: Int-> [Complex Double]
mkxa num = mkTerm num 1
mkxb num = zipWith (+) (mkxa num) (mkTerm num 3)
mkxc num = zipWith (+) (mkxb num) (mkTerm num 5)
printComplexL :: [Complex Double] -> IO ()
printComplexL xs  =
  let  f (i,rl:+im) = 
            do  putStr (spaces (3 - length (show i))  )
                putStr (show i       ++ ":  ("        )
                putStr (niceNum rl  ++ ", "           )
                putStr (niceNum im  ++ ")\n"          )
  in mapM_ f (zip [0..length xs - 1] xs)

niceNum :: Double -> String
niceNum d =
  let  d' = fromIntegral (round (1e10 * d)) / 1e10
       (dec, fra)  = break (== '.') (show d')
       (fra',exp)  = break (== 'e') fra
  in  spaces (3  - length dec) ++ dec ++ take 11 fra'
      ++ exp ++ spaces (12 - length fra' - length exp)

spaces :: Int -> String
spaces  n = take n (repeat ' ')
mkPulse :: Int -> [Complex Double]
mkPulse n = 100 : take (n-1) (repeat 0)
x1 num = let f = pi * 2 * pi / fromIntegral num
         in map (:+ 0) [  sin (f * fromIntegral i)
                          | i <- [0,1..num-1] ]
mkPolars :: [Complex Double] -> [Complex Double]
mkPolars = map ((\(m,p)-> m:+p) . polar)