749 lines
24 KiB
Java
749 lines
24 KiB
Java
/*
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* Copyright (c) 2007, 2013, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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package com.sun.media.sound;
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/**
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* Fast Fourier Transformer.
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*
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* @author Karl Helgason
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*/
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public final class FFT {
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private final double[] w;
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private final int fftFrameSize;
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private final int sign;
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private final int[] bitm_array;
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private final int fftFrameSize2;
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// Sign = -1 is FFT, 1 is IFFT (inverse FFT)
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// Data = Interlaced double array to be transformed.
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// The order is: real (sin), complex (cos)
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// Framesize must be power of 2
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public FFT(int fftFrameSize, int sign) {
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w = computeTwiddleFactors(fftFrameSize, sign);
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this.fftFrameSize = fftFrameSize;
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this.sign = sign;
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fftFrameSize2 = fftFrameSize << 1;
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// Pre-process Bit-Reversal
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bitm_array = new int[fftFrameSize2];
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for (int i = 2; i < fftFrameSize2; i += 2) {
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int j;
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int bitm;
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for (bitm = 2, j = 0; bitm < fftFrameSize2; bitm <<= 1) {
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if ((i & bitm) != 0)
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j++;
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j <<= 1;
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}
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bitm_array[i] = j;
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}
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}
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public void transform(double[] data) {
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bitreversal(data);
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calc(fftFrameSize, data, sign, w);
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}
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private final static double[] computeTwiddleFactors(int fftFrameSize,
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int sign) {
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int imax = (int) (Math.log(fftFrameSize) / Math.log(2.));
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double[] warray = new double[(fftFrameSize - 1) * 4];
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int w_index = 0;
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for (int i = 0, nstep = 2; i < imax; i++) {
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int jmax = nstep;
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nstep <<= 1;
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double wr = 1.0;
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double wi = 0.0;
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double arg = Math.PI / (jmax >> 1);
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double wfr = Math.cos(arg);
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double wfi = sign * Math.sin(arg);
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for (int j = 0; j < jmax; j += 2) {
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warray[w_index++] = wr;
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warray[w_index++] = wi;
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double tempr = wr;
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wr = tempr * wfr - wi * wfi;
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wi = tempr * wfi + wi * wfr;
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}
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}
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// PRECOMPUTATION of wwr1, wwi1 for factor 4 Decomposition (3 * complex
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// operators and 8 +/- complex operators)
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{
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w_index = 0;
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int w_index2 = warray.length >> 1;
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for (int i = 0, nstep = 2; i < (imax - 1); i++) {
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int jmax = nstep;
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nstep *= 2;
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int ii = w_index + jmax;
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for (int j = 0; j < jmax; j += 2) {
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double wr = warray[w_index++];
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double wi = warray[w_index++];
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double wr1 = warray[ii++];
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double wi1 = warray[ii++];
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warray[w_index2++] = wr * wr1 - wi * wi1;
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warray[w_index2++] = wr * wi1 + wi * wr1;
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}
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}
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}
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return warray;
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}
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private final static void calc(int fftFrameSize, double[] data, int sign,
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double[] w) {
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final int fftFrameSize2 = fftFrameSize << 1;
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int nstep = 2;
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if (nstep >= fftFrameSize2)
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return;
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int i = nstep - 2;
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if (sign == -1)
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calcF4F(fftFrameSize, data, i, nstep, w);
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else
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calcF4I(fftFrameSize, data, i, nstep, w);
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}
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private final static void calcF2E(int fftFrameSize, double[] data, int i,
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int nstep, double[] w) {
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int jmax = nstep;
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for (int n = 0; n < jmax; n += 2) {
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double wr = w[i++];
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double wi = w[i++];
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int m = n + jmax;
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double datam_r = data[m];
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double datam_i = data[m + 1];
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double datan_r = data[n];
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double datan_i = data[n + 1];
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double tempr = datam_r * wr - datam_i * wi;
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double tempi = datam_r * wi + datam_i * wr;
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data[m] = datan_r - tempr;
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data[m + 1] = datan_i - tempi;
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data[n] = datan_r + tempr;
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data[n + 1] = datan_i + tempi;
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}
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return;
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}
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// Perform Factor-4 Decomposition with 3 * complex operators and 8 +/-
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// complex operators
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private final static void calcF4F(int fftFrameSize, double[] data, int i,
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int nstep, double[] w) {
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final int fftFrameSize2 = fftFrameSize << 1; // 2*fftFrameSize;
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// Factor-4 Decomposition
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int w_len = w.length >> 1;
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while (nstep < fftFrameSize2) {
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if (nstep << 2 == fftFrameSize2) {
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// Goto Factor-4 Final Decomposition
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// calcF4E(data, i, nstep, -1, w);
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calcF4FE(fftFrameSize, data, i, nstep, w);
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return;
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}
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int jmax = nstep;
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int nnstep = nstep << 1;
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if (nnstep == fftFrameSize2) {
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// Factor-4 Decomposition not possible
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calcF2E(fftFrameSize, data, i, nstep, w);
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return;
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}
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nstep <<= 2;
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int ii = i + jmax;
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int iii = i + w_len;
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{
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i += 2;
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ii += 2;
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iii += 2;
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for (int n = 0; n < fftFrameSize2; n += nstep) {
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int m = n + jmax;
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double datam1_r = data[m];
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double datam1_i = data[m + 1];
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double datan1_r = data[n];
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double datan1_i = data[n + 1];
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n += nnstep;
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m += nnstep;
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double datam2_r = data[m];
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double datam2_i = data[m + 1];
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double datan2_r = data[n];
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double datan2_i = data[n + 1];
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double tempr = datam1_r;
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double tempi = datam1_i;
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datam1_r = datan1_r - tempr;
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datam1_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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double n2w1r = datan2_r;
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double n2w1i = datan2_i;
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double m2ww1r = datam2_r;
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double m2ww1i = datam2_i;
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tempr = m2ww1r - n2w1r;
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tempi = m2ww1i - n2w1i;
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datam2_r = datam1_r + tempi;
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datam2_i = datam1_i - tempr;
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datam1_r = datam1_r - tempi;
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datam1_i = datam1_i + tempr;
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tempr = n2w1r + m2ww1r;
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tempi = n2w1i + m2ww1i;
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datan2_r = datan1_r - tempr;
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datan2_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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data[m] = datam2_r;
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data[m + 1] = datam2_i;
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data[n] = datan2_r;
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data[n + 1] = datan2_i;
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n -= nnstep;
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m -= nnstep;
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data[m] = datam1_r;
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data[m + 1] = datam1_i;
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data[n] = datan1_r;
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data[n + 1] = datan1_i;
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}
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}
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for (int j = 2; j < jmax; j += 2) {
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double wr = w[i++];
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double wi = w[i++];
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double wr1 = w[ii++];
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double wi1 = w[ii++];
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double wwr1 = w[iii++];
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double wwi1 = w[iii++];
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// double wwr1 = wr * wr1 - wi * wi1; // these numbers can be
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// precomputed!!!
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// double wwi1 = wr * wi1 + wi * wr1;
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for (int n = j; n < fftFrameSize2; n += nstep) {
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int m = n + jmax;
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double datam1_r = data[m];
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double datam1_i = data[m + 1];
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double datan1_r = data[n];
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double datan1_i = data[n + 1];
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n += nnstep;
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m += nnstep;
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double datam2_r = data[m];
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double datam2_i = data[m + 1];
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double datan2_r = data[n];
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double datan2_i = data[n + 1];
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double tempr = datam1_r * wr - datam1_i * wi;
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double tempi = datam1_r * wi + datam1_i * wr;
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datam1_r = datan1_r - tempr;
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datam1_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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double n2w1r = datan2_r * wr1 - datan2_i * wi1;
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double n2w1i = datan2_r * wi1 + datan2_i * wr1;
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double m2ww1r = datam2_r * wwr1 - datam2_i * wwi1;
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double m2ww1i = datam2_r * wwi1 + datam2_i * wwr1;
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tempr = m2ww1r - n2w1r;
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tempi = m2ww1i - n2w1i;
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datam2_r = datam1_r + tempi;
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datam2_i = datam1_i - tempr;
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datam1_r = datam1_r - tempi;
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datam1_i = datam1_i + tempr;
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tempr = n2w1r + m2ww1r;
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tempi = n2w1i + m2ww1i;
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datan2_r = datan1_r - tempr;
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datan2_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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data[m] = datam2_r;
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data[m + 1] = datam2_i;
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data[n] = datan2_r;
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data[n + 1] = datan2_i;
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n -= nnstep;
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m -= nnstep;
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data[m] = datam1_r;
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data[m + 1] = datam1_i;
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data[n] = datan1_r;
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data[n + 1] = datan1_i;
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}
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}
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i += jmax << 1;
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}
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calcF2E(fftFrameSize, data, i, nstep, w);
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}
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// Perform Factor-4 Decomposition with 3 * complex operators and 8 +/-
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// complex operators
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private final static void calcF4I(int fftFrameSize, double[] data, int i,
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int nstep, double[] w) {
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final int fftFrameSize2 = fftFrameSize << 1; // 2*fftFrameSize;
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// Factor-4 Decomposition
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int w_len = w.length >> 1;
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while (nstep < fftFrameSize2) {
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if (nstep << 2 == fftFrameSize2) {
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// Goto Factor-4 Final Decomposition
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// calcF4E(data, i, nstep, 1, w);
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calcF4IE(fftFrameSize, data, i, nstep, w);
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return;
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}
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int jmax = nstep;
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int nnstep = nstep << 1;
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if (nnstep == fftFrameSize2) {
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// Factor-4 Decomposition not possible
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calcF2E(fftFrameSize, data, i, nstep, w);
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return;
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}
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nstep <<= 2;
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int ii = i + jmax;
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int iii = i + w_len;
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{
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i += 2;
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ii += 2;
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iii += 2;
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for (int n = 0; n < fftFrameSize2; n += nstep) {
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int m = n + jmax;
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double datam1_r = data[m];
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double datam1_i = data[m + 1];
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double datan1_r = data[n];
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double datan1_i = data[n + 1];
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n += nnstep;
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m += nnstep;
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double datam2_r = data[m];
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double datam2_i = data[m + 1];
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double datan2_r = data[n];
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double datan2_i = data[n + 1];
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double tempr = datam1_r;
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double tempi = datam1_i;
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datam1_r = datan1_r - tempr;
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datam1_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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double n2w1r = datan2_r;
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double n2w1i = datan2_i;
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double m2ww1r = datam2_r;
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double m2ww1i = datam2_i;
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tempr = n2w1r - m2ww1r;
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tempi = n2w1i - m2ww1i;
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datam2_r = datam1_r + tempi;
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datam2_i = datam1_i - tempr;
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datam1_r = datam1_r - tempi;
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datam1_i = datam1_i + tempr;
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tempr = n2w1r + m2ww1r;
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tempi = n2w1i + m2ww1i;
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datan2_r = datan1_r - tempr;
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datan2_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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data[m] = datam2_r;
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data[m + 1] = datam2_i;
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data[n] = datan2_r;
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data[n + 1] = datan2_i;
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n -= nnstep;
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m -= nnstep;
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data[m] = datam1_r;
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data[m + 1] = datam1_i;
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data[n] = datan1_r;
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data[n + 1] = datan1_i;
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}
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}
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for (int j = 2; j < jmax; j += 2) {
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double wr = w[i++];
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double wi = w[i++];
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double wr1 = w[ii++];
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double wi1 = w[ii++];
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double wwr1 = w[iii++];
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double wwi1 = w[iii++];
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// double wwr1 = wr * wr1 - wi * wi1; // these numbers can be
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// precomputed!!!
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// double wwi1 = wr * wi1 + wi * wr1;
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for (int n = j; n < fftFrameSize2; n += nstep) {
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int m = n + jmax;
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double datam1_r = data[m];
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double datam1_i = data[m + 1];
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double datan1_r = data[n];
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double datan1_i = data[n + 1];
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n += nnstep;
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m += nnstep;
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double datam2_r = data[m];
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double datam2_i = data[m + 1];
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double datan2_r = data[n];
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double datan2_i = data[n + 1];
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double tempr = datam1_r * wr - datam1_i * wi;
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double tempi = datam1_r * wi + datam1_i * wr;
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datam1_r = datan1_r - tempr;
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datam1_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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double n2w1r = datan2_r * wr1 - datan2_i * wi1;
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double n2w1i = datan2_r * wi1 + datan2_i * wr1;
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double m2ww1r = datam2_r * wwr1 - datam2_i * wwi1;
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double m2ww1i = datam2_r * wwi1 + datam2_i * wwr1;
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tempr = n2w1r - m2ww1r;
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tempi = n2w1i - m2ww1i;
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datam2_r = datam1_r + tempi;
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datam2_i = datam1_i - tempr;
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datam1_r = datam1_r - tempi;
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datam1_i = datam1_i + tempr;
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tempr = n2w1r + m2ww1r;
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tempi = n2w1i + m2ww1i;
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datan2_r = datan1_r - tempr;
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datan2_i = datan1_i - tempi;
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datan1_r = datan1_r + tempr;
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datan1_i = datan1_i + tempi;
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data[m] = datam2_r;
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data[m + 1] = datam2_i;
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data[n] = datan2_r;
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data[n + 1] = datan2_i;
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n -= nnstep;
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m -= nnstep;
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data[m] = datam1_r;
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data[m + 1] = datam1_i;
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data[n] = datan1_r;
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|
data[n + 1] = datan1_i;
|
|
|
|
}
|
|
}
|
|
|
|
i += jmax << 1;
|
|
|
|
}
|
|
|
|
calcF2E(fftFrameSize, data, i, nstep, w);
|
|
|
|
}
|
|
|
|
// Perform Factor-4 Decomposition with 3 * complex operators and 8 +/-
|
|
// complex operators
|
|
private final static void calcF4FE(int fftFrameSize, double[] data, int i,
|
|
int nstep, double[] w) {
|
|
final int fftFrameSize2 = fftFrameSize << 1; // 2*fftFrameSize;
|
|
// Factor-4 Decomposition
|
|
|
|
int w_len = w.length >> 1;
|
|
while (nstep < fftFrameSize2) {
|
|
|
|
int jmax = nstep;
|
|
int nnstep = nstep << 1;
|
|
if (nnstep == fftFrameSize2) {
|
|
// Factor-4 Decomposition not possible
|
|
calcF2E(fftFrameSize, data, i, nstep, w);
|
|
return;
|
|
}
|
|
nstep <<= 2;
|
|
int ii = i + jmax;
|
|
int iii = i + w_len;
|
|
for (int n = 0; n < jmax; n += 2) {
|
|
double wr = w[i++];
|
|
double wi = w[i++];
|
|
double wr1 = w[ii++];
|
|
double wi1 = w[ii++];
|
|
double wwr1 = w[iii++];
|
|
double wwi1 = w[iii++];
|
|
// double wwr1 = wr * wr1 - wi * wi1; // these numbers can be
|
|
// precomputed!!!
|
|
// double wwi1 = wr * wi1 + wi * wr1;
|
|
|
|
int m = n + jmax;
|
|
|
|
double datam1_r = data[m];
|
|
double datam1_i = data[m + 1];
|
|
double datan1_r = data[n];
|
|
double datan1_i = data[n + 1];
|
|
|
|
n += nnstep;
|
|
m += nnstep;
|
|
double datam2_r = data[m];
|
|
double datam2_i = data[m + 1];
|
|
double datan2_r = data[n];
|
|
double datan2_i = data[n + 1];
|
|
|
|
double tempr = datam1_r * wr - datam1_i * wi;
|
|
double tempi = datam1_r * wi + datam1_i * wr;
|
|
|
|
datam1_r = datan1_r - tempr;
|
|
datam1_i = datan1_i - tempi;
|
|
datan1_r = datan1_r + tempr;
|
|
datan1_i = datan1_i + tempi;
|
|
|
|
double n2w1r = datan2_r * wr1 - datan2_i * wi1;
|
|
double n2w1i = datan2_r * wi1 + datan2_i * wr1;
|
|
double m2ww1r = datam2_r * wwr1 - datam2_i * wwi1;
|
|
double m2ww1i = datam2_r * wwi1 + datam2_i * wwr1;
|
|
|
|
tempr = m2ww1r - n2w1r;
|
|
tempi = m2ww1i - n2w1i;
|
|
|
|
datam2_r = datam1_r + tempi;
|
|
datam2_i = datam1_i - tempr;
|
|
datam1_r = datam1_r - tempi;
|
|
datam1_i = datam1_i + tempr;
|
|
|
|
tempr = n2w1r + m2ww1r;
|
|
tempi = n2w1i + m2ww1i;
|
|
|
|
datan2_r = datan1_r - tempr;
|
|
datan2_i = datan1_i - tempi;
|
|
datan1_r = datan1_r + tempr;
|
|
datan1_i = datan1_i + tempi;
|
|
|
|
data[m] = datam2_r;
|
|
data[m + 1] = datam2_i;
|
|
data[n] = datan2_r;
|
|
data[n + 1] = datan2_i;
|
|
|
|
n -= nnstep;
|
|
m -= nnstep;
|
|
data[m] = datam1_r;
|
|
data[m + 1] = datam1_i;
|
|
data[n] = datan1_r;
|
|
data[n + 1] = datan1_i;
|
|
|
|
}
|
|
|
|
i += jmax << 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
// Perform Factor-4 Decomposition with 3 * complex operators and 8 +/-
|
|
// complex operators
|
|
private final static void calcF4IE(int fftFrameSize, double[] data, int i,
|
|
int nstep, double[] w) {
|
|
final int fftFrameSize2 = fftFrameSize << 1; // 2*fftFrameSize;
|
|
// Factor-4 Decomposition
|
|
|
|
int w_len = w.length >> 1;
|
|
while (nstep < fftFrameSize2) {
|
|
|
|
int jmax = nstep;
|
|
int nnstep = nstep << 1;
|
|
if (nnstep == fftFrameSize2) {
|
|
// Factor-4 Decomposition not possible
|
|
calcF2E(fftFrameSize, data, i, nstep, w);
|
|
return;
|
|
}
|
|
nstep <<= 2;
|
|
int ii = i + jmax;
|
|
int iii = i + w_len;
|
|
for (int n = 0; n < jmax; n += 2) {
|
|
double wr = w[i++];
|
|
double wi = w[i++];
|
|
double wr1 = w[ii++];
|
|
double wi1 = w[ii++];
|
|
double wwr1 = w[iii++];
|
|
double wwi1 = w[iii++];
|
|
// double wwr1 = wr * wr1 - wi * wi1; // these numbers can be
|
|
// precomputed!!!
|
|
// double wwi1 = wr * wi1 + wi * wr1;
|
|
|
|
int m = n + jmax;
|
|
|
|
double datam1_r = data[m];
|
|
double datam1_i = data[m + 1];
|
|
double datan1_r = data[n];
|
|
double datan1_i = data[n + 1];
|
|
|
|
n += nnstep;
|
|
m += nnstep;
|
|
double datam2_r = data[m];
|
|
double datam2_i = data[m + 1];
|
|
double datan2_r = data[n];
|
|
double datan2_i = data[n + 1];
|
|
|
|
double tempr = datam1_r * wr - datam1_i * wi;
|
|
double tempi = datam1_r * wi + datam1_i * wr;
|
|
|
|
datam1_r = datan1_r - tempr;
|
|
datam1_i = datan1_i - tempi;
|
|
datan1_r = datan1_r + tempr;
|
|
datan1_i = datan1_i + tempi;
|
|
|
|
double n2w1r = datan2_r * wr1 - datan2_i * wi1;
|
|
double n2w1i = datan2_r * wi1 + datan2_i * wr1;
|
|
double m2ww1r = datam2_r * wwr1 - datam2_i * wwi1;
|
|
double m2ww1i = datam2_r * wwi1 + datam2_i * wwr1;
|
|
|
|
tempr = n2w1r - m2ww1r;
|
|
tempi = n2w1i - m2ww1i;
|
|
|
|
datam2_r = datam1_r + tempi;
|
|
datam2_i = datam1_i - tempr;
|
|
datam1_r = datam1_r - tempi;
|
|
datam1_i = datam1_i + tempr;
|
|
|
|
tempr = n2w1r + m2ww1r;
|
|
tempi = n2w1i + m2ww1i;
|
|
|
|
datan2_r = datan1_r - tempr;
|
|
datan2_i = datan1_i - tempi;
|
|
datan1_r = datan1_r + tempr;
|
|
datan1_i = datan1_i + tempi;
|
|
|
|
data[m] = datam2_r;
|
|
data[m + 1] = datam2_i;
|
|
data[n] = datan2_r;
|
|
data[n + 1] = datan2_i;
|
|
|
|
n -= nnstep;
|
|
m -= nnstep;
|
|
data[m] = datam1_r;
|
|
data[m + 1] = datam1_i;
|
|
data[n] = datan1_r;
|
|
data[n + 1] = datan1_i;
|
|
|
|
}
|
|
|
|
i += jmax << 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
private final void bitreversal(double[] data) {
|
|
if (fftFrameSize < 4)
|
|
return;
|
|
|
|
int inverse = fftFrameSize2 - 2;
|
|
for (int i = 0; i < fftFrameSize; i += 4) {
|
|
int j = bitm_array[i];
|
|
|
|
// Performing Bit-Reversal, even v.s. even, O(2N)
|
|
if (i < j) {
|
|
|
|
int n = i;
|
|
int m = j;
|
|
|
|
// COMPLEX: SWAP(data[n], data[m])
|
|
// Real Part
|
|
double tempr = data[n];
|
|
data[n] = data[m];
|
|
data[m] = tempr;
|
|
// Imagery Part
|
|
n++;
|
|
m++;
|
|
double tempi = data[n];
|
|
data[n] = data[m];
|
|
data[m] = tempi;
|
|
|
|
n = inverse - i;
|
|
m = inverse - j;
|
|
|
|
// COMPLEX: SWAP(data[n], data[m])
|
|
// Real Part
|
|
tempr = data[n];
|
|
data[n] = data[m];
|
|
data[m] = tempr;
|
|
// Imagery Part
|
|
n++;
|
|
m++;
|
|
tempi = data[n];
|
|
data[n] = data[m];
|
|
data[m] = tempi;
|
|
}
|
|
|
|
// Performing Bit-Reversal, odd v.s. even, O(N)
|
|
|
|
int m = j + fftFrameSize; // bitm_array[i+2];
|
|
// COMPLEX: SWAP(data[n], data[m])
|
|
// Real Part
|
|
int n = i + 2;
|
|
double tempr = data[n];
|
|
data[n] = data[m];
|
|
data[m] = tempr;
|
|
// Imagery Part
|
|
n++;
|
|
m++;
|
|
double tempi = data[n];
|
|
data[n] = data[m];
|
|
data[m] = tempi;
|
|
}
|
|
|
|
}
|
|
}
|