Discrete Fourier transform in CoffeeScript.

discrete_fourier_transform.coffee

 {cos, sin, sqrt} = Math
 τ = 2 * Math.PI

 DFT = (series) ->
   N = series.length
   rootN = sqrt(N)
   divRootN = (x) -> x / rootN

   [0...N].map (k) ->
     series.map ([x, y], n) ->
       theta = -τ * k * n / N
       [
         x *  cos(theta) + y *  sin(theta)
         x * -sin(theta) + y * -cos(theta)
       ]
     .reduce((a, b) ->
       [a[0] + b[0], a[1] + b[1]]
     , [0, 0])
     .map divRootN