module FastFourier

The MIT License (MIT)

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Constants

VERSION

Public Class Methods

dft(vals, inverse = false)

Alias for: discrete_fourier

discrete_fourier(vals, inverse = false) click to toggle source

# File lib/fast-fourier/fast-fourier.rb, line 35
def FastFourier.discrete_fourier(vals, inverse = false)
  n = vals.length
  if(n % 2 == 0)
    dft =  :cooley_tukey_dft
  else
    dft = :discrete_fourier_slow
  end

  if inverse
    case inverse
      when :conjugate
        send( dft, vals.map { |x| x.conj } ).map {|x| x.conj / vals.length}
      when :swap
        send( dft,  vals.map { |x| Complex(x.imag, x.real) } ).map {|x| Complex(x.imag, x.real) / vals.length}
      else
        send( dft, [vals[0]] + vals[1..-1].reverse).map{|x| x / vals.length}
    end
  else
    send( dft, vals)
  end
end

Also aliased as: dft

discrete_involutary(vals) click to toggle source

This is a self-inverse variation of the discrete fourier transform

# File lib/fast-fourier/fast-fourier.rb, line 62
def FastFourier.discrete_involutary(vals)
      n = vals.length
  if(n % 2 == 0)
    dft =  :cooley_tukey_dft
  else
    dft = :discrete_fourier_slow
  end

  result = send( dft, vals.map { |x| x.conj } ).map {|x| x / Math.sqrt(vals.length) }

  result[0...n]    
end

Private Class Methods

cooley_tukey_dft(vals) click to toggle source

# File lib/fast-fourier/fast-fourier.rb, line 87
def FastFourier.cooley_tukey_dft(vals)
  if vals.size == 1
    vals
  else
    n = vals.length
    if(n % 2 == 0) # if n is not a power of 2
      dft =  :cooley_tukey_dft
    else
      dft = :discrete_fourier_slow
    end
    vals_even = send( dft, (0...n).step(2).map{|i| vals[i]})
    vals_odd = send( dft, (1...n).step(2).map{|i| vals[i]})

    ret_vals = Array.new(n)

    (0...(n/2)).each do |i|
      ei = vals_even[i]
      oi = vals_odd[i]
      npri = root_of_unity(n, i).conj
      oink = npri * oi
      ret_vals[i] = (ei + oink)
      ret_vals[i+n/2] = (ei - oink)
    end
    ret_vals
  end
end

discrete_fourier_slow(vals, inverse=false) click to toggle source

# File lib/fast-fourier/fast-fourier.rb, line 114
def FastFourier.discrete_fourier_slow(vals, inverse=false)
  npr = root_of_unity(vals.length)
  (0...(vals.length)).map do |i|
    ary = (0...(vals.length)).map do |j|
      vals[j] * npr ** (-1*i*j)
    end
    ary.inject(:+)
  end
end

root_of_unity(den, num = 1) click to toggle source

# File lib/fast-fourier/fast-fourier.rb, line 77
def FastFourier.root_of_unity(den, num = 1)
  key = Rational(num, den) % 1
  if ans = @@fast_fourier_roots[key]
    ans
  else
    angle = 2*Math::PI * key
    @@fast_fourier_roots[key] = Complex(Math.cos(angle), Math.sin(angle))
  end
end