Chris@0: /* 
Chris@0:  * Free FFT and convolution (JavaScript)
Chris@0:  * 
Chris@0:  * Copyright (c) 2014 Project Nayuki
Chris@0:  * http://www.nayuki.io/page/free-small-fft-in-multiple-languages
Chris@24:  *
Chris@0:  * (MIT License)
Chris@0:  * Permission is hereby granted, free of charge, to any person obtaining a copy of
Chris@0:  * this software and associated documentation files (the "Software"), to deal in
Chris@0:  * the Software without restriction, including without limitation the rights to
Chris@0:  * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
Chris@0:  * the Software, and to permit persons to whom the Software is furnished to do so,
Chris@0:  * subject to the following conditions:
Chris@0:  * - The above copyright notice and this permission notice shall be included in
Chris@0:  *   all copies or substantial portions of the Software.
Chris@0:  * - The Software is provided "as is", without warranty of any kind, express or
Chris@0:  *   implied, including but not limited to the warranties of merchantability,
Chris@0:  *   fitness for a particular purpose and noninfringement. In no event shall the
Chris@0:  *   authors or copyright holders be liable for any claim, damages or other
Chris@0:  *   liability, whether in an action of contract, tort or otherwise, arising from,
Chris@0:  *   out of or in connection with the Software or the use or other dealings in the
Chris@0:  *   Software.
Chris@24:  *
Chris@24:  * Slightly restructured by Chris Cannam, cannam@all-day-breakfast.com
Chris@0:  */
Chris@0: 
Chris@0: "use strict";
Chris@0: 
Chris@24: /* 
Chris@24:  * Construct an object for calculating the discrete Fourier transform (DFT) of size n, where n is a power of 2.
Chris@24:  */
Chris@17: function FFTNayuki(n) {
Chris@19:     
Chris@17:     this.n = n;
Chris@17:     this.levels = -1;
Chris@0: 
Chris@17:     for (var i = 0; i < 32; i++) {
Chris@17:         if (1 << i == n) {
Chris@17:             this.levels = i;  // Equal to log2(n)
Chris@17: 	}
Chris@17:     }
Chris@17:     if (this.levels == -1) {
Chris@17:         throw "Length is not a power of 2";
Chris@17:     }
Chris@17: 
Chris@17:     this.cosTable = new Array(n / 2);
Chris@17:     this.sinTable = new Array(n / 2);
Chris@17:     for (var i = 0; i < n / 2; i++) {
Chris@17:         this.cosTable[i] = Math.cos(2 * Math.PI * i / n);
Chris@17:         this.sinTable[i] = Math.sin(2 * Math.PI * i / n);
Chris@17:     }
Chris@17: 
Chris@24:     /* 
Chris@24:      * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
Chris@24:      * 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.
Chris@24:      */
Chris@17:     this.forward = function(real, imag) {
Chris@22: 
Chris@22: 	var n = this.n;
Chris@17: 	
Chris@24: 	// Bit-reversed addressing permutation
Chris@17: 	for (var i = 0; i < n; i++) {
Chris@17:             var j = reverseBits(i, this.levels);
Chris@17:             if (j > i) {
Chris@17: 		var temp = real[i];
Chris@17: 		real[i] = real[j];
Chris@17: 		real[j] = temp;
Chris@17: 		temp = imag[i];
Chris@17: 		imag[i] = imag[j];
Chris@17: 		imag[j] = temp;
Chris@17:             }
Chris@17: 	}
Chris@0:     
Chris@24: 	// Cooley-Tukey decimation-in-time radix-2 FFT
Chris@17: 	for (var size = 2; size <= n; size *= 2) {
Chris@17:             var halfsize = size / 2;
Chris@17:             var tablestep = n / size;
Chris@17:             for (var i = 0; i < n; i += size) {
Chris@17: 		for (var j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
Chris@17:                     var tpre =  real[j+halfsize] * this.cosTable[k] +
Chris@17: 			        imag[j+halfsize] * this.sinTable[k];
Chris@17:                     var tpim = -real[j+halfsize] * this.sinTable[k] +
Chris@17: 			        imag[j+halfsize] * this.cosTable[k];
Chris@17:                     real[j + halfsize] = real[j] - tpre;
Chris@17:                     imag[j + halfsize] = imag[j] - tpim;
Chris@17:                     real[j] += tpre;
Chris@17:                     imag[j] += tpim;
Chris@17: 		}
Chris@17:             }
Chris@17: 	}
Chris@17:     
Chris@24: 	// Returns the integer whose value is the reverse of the lowest 'bits' bits of the integer 'x'.
Chris@17: 	function reverseBits(x, bits) {
Chris@17:             var y = 0;
Chris@17:             for (var i = 0; i < bits; i++) {
Chris@17: 		y = (y << 1) | (x & 1);
Chris@17: 		x >>>= 1;
Chris@17:             }
Chris@17:             return y;
Chris@17: 	}
Chris@17:     }
Chris@0: 
Chris@24:     /* 
Chris@24:      * Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector.
Chris@24:      * 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.
Chris@24:      */
Chris@17:     this.inverse = function(real, imag) {
Chris@17: 	forward(imag, real);
Chris@0:     }
Chris@0: }
Chris@0: