module FastFourier

The MIT License (MIT)

Copyright © 2014 Justin W, Smith

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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