{-# OPTIONS_GHC -Wall #-}

module Examples where

import Data.Complex.Cyclotomic
import Data.Ratio

-- | A Discrete Fourier Transform
dft :: [Cyclotomic] -> [Cyclotomic]
dft cs = [sum $ zipWith (*) [conj (e m^(k*n)) | n <- [0..]] cs | k <- [0..m-1]]
          where m = fromIntegral $ length cs

-- | Inverse Discrete Fourier Transform
dftInv :: [Cyclotomic] -> [Cyclotomic]
dftInv cs = [minv * sum (zipWith (*) [e m^(k*n) | n <- [0..]] cs) | k <- [0..m-1]]
          where m = fromIntegral $ length cs
                minv = fromRational (1 % m)