kopia lustrzana https://github.com/ag1le/morse-wip
805 wiersze
20 KiB
C++
805 wiersze
20 KiB
C++
//===========================================================================
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// Real Discrete Fourier Transform
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// dimension :one
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// data length :power of 2, must be larger than 4
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// decimation :frequency
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// radix :4, 2
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// data :inplace
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// classes:
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// Cfft: real discrete fourier transform class
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// functions:
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// Cfft::rdft : compute the forward real discrete fourier transform
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// Cfft::cdft : compute the forward double discrete fourier transform
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// Cfft::icdft : compute the reverse double discrete fourier transform
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// Cfft::fft : compute the forward real dft on a set of integer values
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//
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// This class is derived from the work of Takuya Ooura, who has kindly put his
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// fft algorithims in the public domain. Thank you Takuya Ooura!
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//===========================================================================
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#include <config.h>
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#include "misc.h"
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#include "fft.h"
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// n = size of fourier transform in complex pairs
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// fftsiz = size of fourier transform in real (double) values
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Cfft::Cfft(int n)
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{
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int tablesize = (int)(sqrt(n*1.0)+0.5) + 2;
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fftlen = n;
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fftsiz = 2 * n;
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ip = new int[tablesize];
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w = new double[fftlen];
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fftwin = new double[fftlen*2];
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makewt();
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makect();
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wintype = FFT_NONE;
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RectWindow(fftwin, fftlen*2);
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}
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Cfft::~Cfft()
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{
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if (ip) delete [] ip;
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if (w) delete [] w;
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if (fftwin) delete [] fftwin;
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}
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void Cfft::resize(int n)
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{
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int tablesize = (int)(sqrt(n*1.0)+0.5) + 2;
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fftlen = n;
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fftsiz = 2 * n;
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if (ip) delete [] ip;
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ip = new int[tablesize];
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if (w) delete [] w;
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w = new double[fftlen];
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if (fftwin) delete [] fftwin;
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fftwin = new double[fftlen*2];
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makewt();
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makect();
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wintype = FFT_NONE;
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RectWindow(fftwin, fftlen*2);
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}
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void Cfft::cdft(double *aCmpx)
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{
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if (wintype != FFT_NONE)
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for (int i = 0; i < fftlen; i++) {
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aCmpx[2*i] *= fftwin[2*i];
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aCmpx[2*i+1] *= fftwin[2*i];
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}
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bitrv2(fftsiz, ip + 2, aCmpx);
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cftfsub(fftsiz, aCmpx);
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double scale = 1.0 / fftlen;
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for (int i = 0; i < fftsiz; i++) aCmpx[i] = aCmpx[i] * scale;
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}
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void Cfft::icdft(double *aCmpx)
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{
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bitrv2conj(fftsiz, ip + 2, aCmpx);
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cftbsub(fftsiz, aCmpx);
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}
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// FFT of an array of short integers
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// siData = array (size n) of unsigned integers such as the output of a soundcard
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// operating in 16 bit mode
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// out = array (size n) of double pairs
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void Cfft::sifft(short int *siData, double *out)
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{
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for (int i = 0; i < fftlen; i++) {
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out[2*i] = siData[i];
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out[2*i+1] = 0.0;
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}
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cdft(out);
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return;
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}
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void Cfft::rdft(double *RealData) // RealData is 2N long
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{
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if (wintype != FFT_NONE)
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for (int i = 0; i < fftlen*2; i++) {
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RealData[i] *= fftwin[i];
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}
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if (fftsiz > 4) {
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bitrv2(fftsiz, ip + 2, RealData);
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cftfsub(fftsiz, RealData);
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rftfsub(fftsiz, RealData);
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} else if (fftsiz == 4) {
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cftfsub(fftsiz, RealData);
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}
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double xi = RealData[0] - RealData[1];
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RealData[0] += RealData[1];
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RealData[1] = xi;
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double scale = 1.0 / fftlen;
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for (int i = 0; i < fftsiz; i++) RealData[i] *= scale;
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}
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void Cfft::irdft(double *RealData)
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{
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/*
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int nw, nc;
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double xi;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > (nc << 2)) {
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nc = n >> 2;
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makect(nc, ip, w + nw);
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}
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if (isgn >= 0) {
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if (n > 4) {
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bitrv2(n, ip + 2, a);
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cftfsub(n, a, w);
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rftfsub(n, a, nc, w + nw);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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xi = a[0] - a[1];
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a[0] += a[1];
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a[1] = xi;
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} else {
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a[1] = 0.5 * (a[0] - a[1]);
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a[0] -= a[1];
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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bitrv2(n, ip + 2, a);
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cftbsub(n, a, w);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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}
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*/
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}
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void Cfft::setWindow(fftPrefilter pf)
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{
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wintype = pf;
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if (wintype == FFT_TRIANGULAR)
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TriangularWindow(fftwin, fftlen*2);
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else if (wintype == FFT_HAMMING)
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HammingWindow(fftwin, fftlen*2);
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else if (wintype == FFT_HANNING)
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HanningWindow(fftwin, fftlen*2);
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else if (wintype == FFT_BLACKMAN)
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BlackmanWindow(fftwin, fftlen*2);
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else
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RectWindow(fftwin, fftlen*2);
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}
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/* -------- initializing routines -------- */
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void Cfft::makewt()
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{
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int j,
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nwh, nw = fftsiz / 4;
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double delta, x, y;
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ip[0] = nw;
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ip[1] = 1;
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if (nw > 2) {
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nwh = nw >> 1;
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delta = atan(1.0) / nwh;
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w[0] = 1;
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w[1] = 0;
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w[nwh] = cos(delta * nwh);
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w[nwh + 1] = w[nwh];
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if (nwh > 2) {
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for (j = 2; j < nwh; j += 2) {
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x = cos(delta * j);
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y = sin(delta * j);
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w[j] = x;
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w[j + 1] = y;
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w[nw - j] = y;
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w[nw - j + 1] = x;
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}
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bitrv2(nw, ip + 2, w);
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}
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}
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}
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void Cfft::makect()
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{
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int j, nch, nc = fftsiz / 4;
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double delta;
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double *c = w + fftsiz / 4;
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c = w + fftsiz / 4;
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ip[1] = nc;
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if (nc > 1) {
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nch = nc >> 1;
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delta = atan(1.0) / nch;
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c[0] = cos(delta * nch);
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c[nch] = 0.5 * c[0];
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for (j = 1; j < nch; j++) {
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c[j] = 0.5 * cos(delta * j);
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c[nc - j] = 0.5 * sin(delta * j);
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}
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}
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}
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/* -------- child routines -------- */
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void Cfft::bitrv2(int n, int *ip, double *a)
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{
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int j, j1, k, k1, l, m, m2;
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double xr, xi, yr, yi;
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ip[0] = 0;
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l = n;
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m = 1;
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while ((m << 3) < l) {
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l >>= 1;
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for (j = 0; j < m; j++) {
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ip[m + j] = ip[j] + l;
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}
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m <<= 1;
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}
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m2 = 2 * m;
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if ((m << 3) == l) {
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for (k = 0; k < m; k++) {
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for (j = 0; j < k; j++) {
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j1 = 2 * j + ip[k];
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k1 = 2 * k + ip[j];
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m2;
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k1 += 2 * m2;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m2;
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k1 -= m2;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m2;
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k1 += 2 * m2;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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}
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j1 = 2 * k + m2 + ip[k];
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k1 = j1 + m2;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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}
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} else {
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for (k = 1; k < m; k++) {
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for (j = 0; j < k; j++) {
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j1 = 2 * j + ip[k];
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k1 = 2 * k + ip[j];
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m2;
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k1 += m2;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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}
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}
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}
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}
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void Cfft::cftfsub(int n, double *a)
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{
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int j, j1, j2, j3, l;
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double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
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l = 2;
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if (n > 8) {
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cft1st(n, a);
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l = 8;
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while ((l << 2) < n) {
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cftmdl(n, l, a);
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l <<= 2;
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}
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}
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if ((l << 2) == n) {
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for (j = 0; j < l; j += 2) {
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j1 = j + l;
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j2 = j1 + l;
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j3 = j2 + l;
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x0r = a[j] + a[j1];
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x0i = a[j + 1] + a[j1 + 1];
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x1r = a[j] - a[j1];
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x1i = a[j + 1] - a[j1 + 1];
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x2r = a[j2] + a[j3];
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x2i = a[j2 + 1] + a[j3 + 1];
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x3r = a[j2] - a[j3];
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x3i = a[j2 + 1] - a[j3 + 1];
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a[j] = x0r + x2r;
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a[j + 1] = x0i + x2i;
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a[j2] = x0r - x2r;
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a[j2 + 1] = x0i - x2i;
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a[j1] = x1r - x3i;
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a[j1 + 1] = x1i + x3r;
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a[j3] = x1r + x3i;
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a[j3 + 1] = x1i - x3r;
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}
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} else {
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for (j = 0; j < l; j += 2) {
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j1 = j + l;
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x0r = a[j] - a[j1];
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x0i = a[j + 1] - a[j1 + 1];
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a[j] += a[j1];
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a[j + 1] += a[j1 + 1];
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a[j1] = x0r;
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a[j1 + 1] = x0i;
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}
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}
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}
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void Cfft::cft1st(int n, double *a)
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{
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int j, k1, k2;
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double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
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double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
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x0r = a[0] + a[2];
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x0i = a[1] + a[3];
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x1r = a[0] - a[2];
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x1i = a[1] - a[3];
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x2r = a[4] + a[6];
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x2i = a[5] + a[7];
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x3r = a[4] - a[6];
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x3i = a[5] - a[7];
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a[0] = x0r + x2r;
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a[1] = x0i + x2i;
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a[4] = x0r - x2r;
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a[5] = x0i - x2i;
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a[2] = x1r - x3i;
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a[3] = x1i + x3r;
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a[6] = x1r + x3i;
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a[7] = x1i - x3r;
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wk1r = w[2];
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x0r = a[8] + a[10];
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x0i = a[9] + a[11];
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x1r = a[8] - a[10];
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x1i = a[9] - a[11];
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x2r = a[12] + a[14];
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x2i = a[13] + a[15];
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x3r = a[12] - a[14];
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x3i = a[13] - a[15];
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a[8] = x0r + x2r;
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a[9] = x0i + x2i;
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a[12] = x2i - x0i;
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a[13] = x0r - x2r;
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x0r = x1r - x3i;
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x0i = x1i + x3r;
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a[10] = wk1r * (x0r - x0i);
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a[11] = wk1r * (x0r + x0i);
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x0r = x3i + x1r;
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x0i = x3r - x1i;
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a[14] = wk1r * (x0i - x0r);
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a[15] = wk1r * (x0i + x0r);
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k1 = 0;
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for (j = 16; j < n; j += 16) {
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k1 += 2;
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k2 = 2 * k1;
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wk2r = w[k1];
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wk2i = w[k1 + 1];
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wk1r = w[k2];
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wk1i = w[k2 + 1];
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wk3r = wk1r - 2 * wk2i * wk1i;
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wk3i = 2 * wk2i * wk1r - wk1i;
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x0r = a[j] + a[j + 2];
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x0i = a[j + 1] + a[j + 3];
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x1r = a[j] - a[j + 2];
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x1i = a[j + 1] - a[j + 3];
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x2r = a[j + 4] + a[j + 6];
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x2i = a[j + 5] + a[j + 7];
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x3r = a[j + 4] - a[j + 6];
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x3i = a[j + 5] - a[j + 7];
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a[j] = x0r + x2r;
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a[j + 1] = x0i + x2i;
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x0r -= x2r;
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x0i -= x2i;
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a[j + 4] = wk2r * x0r - wk2i * x0i;
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a[j + 5] = wk2r * x0i + wk2i * x0r;
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x0r = x1r - x3i;
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x0i = x1i + x3r;
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a[j + 2] = wk1r * x0r - wk1i * x0i;
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a[j + 3] = wk1r * x0i + wk1i * x0r;
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x0r = x1r + x3i;
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x0i = x1i - x3r;
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a[j + 6] = wk3r * x0r - wk3i * x0i;
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a[j + 7] = wk3r * x0i + wk3i * x0r;
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wk1r = w[k2 + 2];
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wk1i = w[k2 + 3];
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wk3r = wk1r - 2 * wk2r * wk1i;
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wk3i = 2 * wk2r * wk1r - wk1i;
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x0r = a[j + 8] + a[j + 10];
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x0i = a[j + 9] + a[j + 11];
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x1r = a[j + 8] - a[j + 10];
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x1i = a[j + 9] - a[j + 11];
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x2r = a[j + 12] + a[j + 14];
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x2i = a[j + 13] + a[j + 15];
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x3r = a[j + 12] - a[j + 14];
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x3i = a[j + 13] - a[j + 15];
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a[j + 8] = x0r + x2r;
|
|
a[j + 9] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j + 12] = -wk2i * x0r - wk2r * x0i;
|
|
a[j + 13] = -wk2i * x0i + wk2r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j + 10] = wk1r * x0r - wk1i * x0i;
|
|
a[j + 11] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j + 14] = wk3r * x0r - wk3i * x0i;
|
|
a[j + 15] = wk3r * x0i + wk3i * x0r;
|
|
}
|
|
}
|
|
|
|
|
|
void Cfft::cftmdl(int n, int l, double *a)
|
|
{
|
|
int j, j1, j2, j3, k, k1, k2, m, m2;
|
|
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
|
|
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
|
|
|
|
m = l << 2;
|
|
for (j = 0; j < l; j += 2) {
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
a[j2] = x0r - x2r;
|
|
a[j2 + 1] = x0i - x2i;
|
|
a[j1] = x1r - x3i;
|
|
a[j1 + 1] = x1i + x3r;
|
|
a[j3] = x1r + x3i;
|
|
a[j3 + 1] = x1i - x3r;
|
|
}
|
|
wk1r = w[2];
|
|
for (j = m; j < l + m; j += 2) {
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
a[j2] = x2i - x0i;
|
|
a[j2 + 1] = x0r - x2r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j1] = wk1r * (x0r - x0i);
|
|
a[j1 + 1] = wk1r * (x0r + x0i);
|
|
x0r = x3i + x1r;
|
|
x0i = x3r - x1i;
|
|
a[j3] = wk1r * (x0i - x0r);
|
|
a[j3 + 1] = wk1r * (x0i + x0r);
|
|
}
|
|
k1 = 0;
|
|
m2 = 2 * m;
|
|
for (k = m2; k < n; k += m2) {
|
|
k1 += 2;
|
|
k2 = 2 * k1;
|
|
wk2r = w[k1];
|
|
wk2i = w[k1 + 1];
|
|
wk1r = w[k2];
|
|
wk1i = w[k2 + 1];
|
|
wk3r = wk1r - 2 * wk2i * wk1i;
|
|
wk3i = 2 * wk2i * wk1r - wk1i;
|
|
for (j = k; j < l + k; j += 2) {
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j2] = wk2r * x0r - wk2i * x0i;
|
|
a[j2 + 1] = wk2r * x0i + wk2i * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j1] = wk1r * x0r - wk1i * x0i;
|
|
a[j1 + 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3r * x0r - wk3i * x0i;
|
|
a[j3 + 1] = wk3r * x0i + wk3i * x0r;
|
|
}
|
|
wk1r = w[k2 + 2];
|
|
wk1i = w[k2 + 3];
|
|
wk3r = wk1r - 2 * wk2r * wk1i;
|
|
wk3i = 2 * wk2r * wk1r - wk1i;
|
|
for (j = k + m; j < l + (k + m); j += 2) {
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j2] = -wk2i * x0r - wk2r * x0i;
|
|
a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j1] = wk1r * x0r - wk1i * x0i;
|
|
a[j1 + 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3r * x0r - wk3i * x0i;
|
|
a[j3 + 1] = wk3r * x0i + wk3i * x0r;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void Cfft::cftbsub(int n, double *a)
|
|
{
|
|
int j, j1, j2, j3, l;
|
|
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
|
|
|
|
l = 2;
|
|
if (n > 8) {
|
|
cft1st(n, a);
|
|
l = 8;
|
|
while ((l << 2) < n) {
|
|
cftmdl(n, l, a);
|
|
l <<= 2;
|
|
}
|
|
}
|
|
if ((l << 2) == n) {
|
|
for (j = 0; j < l; j += 2) {
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = -a[j + 1] - a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = -a[j + 1] + a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i - x2i;
|
|
a[j2] = x0r - x2r;
|
|
a[j2 + 1] = x0i + x2i;
|
|
a[j1] = x1r - x3i;
|
|
a[j1 + 1] = x1i - x3r;
|
|
a[j3] = x1r + x3i;
|
|
a[j3 + 1] = x1i + x3r;
|
|
}
|
|
} else {
|
|
for (j = 0; j < l; j += 2) {
|
|
j1 = j + l;
|
|
x0r = a[j] - a[j1];
|
|
x0i = -a[j + 1] + a[j1 + 1];
|
|
a[j] += a[j1];
|
|
a[j + 1] = -a[j + 1] - a[j1 + 1];
|
|
a[j1] = x0r;
|
|
a[j1 + 1] = x0i;
|
|
}
|
|
}
|
|
}
|
|
|
|
void Cfft::bitrv2conj(int n, int *ip, double *a)
|
|
{
|
|
int j, j1, k, k1, l, m, m2;
|
|
double xr, xi, yr, yi;
|
|
|
|
ip[0] = 0;
|
|
l = n;
|
|
m = 1;
|
|
while ((m << 3) < l) {
|
|
l >>= 1;
|
|
for (j = 0; j < m; j++) {
|
|
ip[m + j] = ip[j] + l;
|
|
}
|
|
m <<= 1;
|
|
}
|
|
m2 = 2 * m;
|
|
if ((m << 3) == l) {
|
|
for (k = 0; k < m; k++) {
|
|
for (j = 0; j < k; j++) {
|
|
j1 = 2 * j + ip[k];
|
|
k1 = 2 * k + ip[j];
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
j1 += m2;
|
|
k1 += 2 * m2;
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
j1 += m2;
|
|
k1 -= m2;
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
j1 += m2;
|
|
k1 += 2 * m2;
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
}
|
|
k1 = 2 * k + ip[k];
|
|
a[k1 + 1] = -a[k1 + 1];
|
|
j1 = k1 + m2;
|
|
k1 = j1 + m2;
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
k1 += m2;
|
|
a[k1 + 1] = -a[k1 + 1];
|
|
}
|
|
} else {
|
|
a[1] = -a[1];
|
|
a[m2 + 1] = -a[m2 + 1];
|
|
for (k = 1; k < m; k++) {
|
|
for (j = 0; j < k; j++) {
|
|
j1 = 2 * j + ip[k];
|
|
k1 = 2 * k + ip[j];
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
j1 += m2;
|
|
k1 += m2;
|
|
xr = a[j1];
|
|
xi = -a[j1 + 1];
|
|
yr = a[k1];
|
|
yi = -a[k1 + 1];
|
|
a[j1] = yr;
|
|
a[j1 + 1] = yi;
|
|
a[k1] = xr;
|
|
a[k1 + 1] = xi;
|
|
}
|
|
k1 = 2 * k + ip[k];
|
|
a[k1 + 1] = -a[k1 + 1];
|
|
a[k1 + m2 + 1] = -a[k1 + m2 + 1];
|
|
}
|
|
}
|
|
}
|
|
|
|
void Cfft::rftfsub(int n, double *a)
|
|
{
|
|
int j, k, kk, ks, m;
|
|
double wkr, wki, xr, xi, yr, yi;
|
|
double *c = w + fftsiz / 4;
|
|
int nc = n >> 2;
|
|
|
|
m = n >> 1;
|
|
ks = 2 * nc / m;
|
|
kk = 0;
|
|
for (j = 2; j < m; j += 2) {
|
|
k = n - j;
|
|
kk += ks;
|
|
wkr = 0.5 - c[nc - kk];
|
|
wki = c[kk];
|
|
xr = a[j] - a[k];
|
|
xi = a[j + 1] + a[k + 1];
|
|
yr = wkr * xr - wki * xi;
|
|
yi = wkr * xi + wki * xr;
|
|
a[j] -= yr;
|
|
a[j + 1] -= yi;
|
|
a[k] += yr;
|
|
a[k + 1] -= yi;
|
|
}
|
|
}
|
|
|
|
void Cfft::rftbsub(int n, double *a)
|
|
{
|
|
}
|
|
|
|
|
|
|