fft.js

/* 
 * Free FFT and convolution (JavaScript)
 * 
 * Copyright (c) 2014 Project Nayuki
 * http://www.nayuki.io/page/free-small-fft-in-multiple-languages
 *
 * (MIT License)
 * 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.
 *
 * Slightly restructured by Chris Cannam, cannam@all-day-breakfast.com
 */

"use strict";

/* 
 * Construct an object for calculating the discrete Fourier transform (DFT) of size n, where n is a power of 2.
 */
function FFTNayuki(n) {
    
    this.n = n;
    this.levels = -1;

    for (var i = 0; i < 32; i++) {
        if (1 << i == n) {
            this.levels = i;  // Equal to log2(n)
        }
    }
    if (this.levels == -1) {
        throw "Length is not a power of 2";
    }

    this.cosTable = new Array(n / 2);
    this.sinTable = new Array(n / 2);
    for (var i = 0; i < n / 2; i++) {
        this.cosTable[i] = Math.cos(2 * Math.PI * i / n);
        this.sinTable[i] = Math.sin(2 * Math.PI * i / n);
    }

    /* 
     * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
     * The vector's length must be equal to the size n that was passed to the object constructor, and this must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
     */
    this.forward = function(real, imag) {

        var n = this.n;
        
        // Bit-reversed addressing permutation
        for (var i = 0; i < n; i++) {
            var j = reverseBits(i, this.levels);
            if (j > i) {
                var temp = real[i];
                real[i] = real[j];
                real[j] = temp;
                temp = imag[i];
                imag[i] = imag[j];
                imag[j] = temp;
            }
        }
    
        // Cooley-Tukey decimation-in-time radix-2 FFT
        for (var size = 2; size <= n; size *= 2) {
            var halfsize = size / 2;
            var tablestep = n / size;
            for (var i = 0; i < n; i += size) {
                for (var j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
                    var tpre =  real[j+halfsize] * this.cosTable[k] +
                                imag[j+halfsize] * this.sinTable[k];
                    var tpim = -real[j+halfsize] * this.sinTable[k] +
                                imag[j+halfsize] * this.cosTable[k];
                    real[j + halfsize] = real[j] - tpre;
                    imag[j + halfsize] = imag[j] - tpim;
                    real[j] += tpre;
                    imag[j] += tpim;
                }
            }
        }
    
        // Returns the integer whose value is the reverse of the lowest 'bits' bits of the integer 'x'.
        function reverseBits(x, bits) {
            var y = 0;
            for (var i = 0; i < bits; i++) {
                y = (y << 1) | (x & 1);
                x >>>= 1;
            }
            return y;
        }
    }

    /* 
     * Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector.
     * The vector's length must be equal to the size n that was passed to the object constructor, and this must be a power of 2. This is a wrapper function. This transform does not perform scaling, so the inverse is not a true inverse.
     */
    this.inverse = function(real, imag) {
        forward(imag, real);
    }
}