annotate data/model/FFTModel.cpp @ 1236:fe391a7b8376 project-file-rework

Rename server to simple-server, and add some more description in usage
author Chris Cannam
date Fri, 28 Oct 2016 11:08:17 +0100
parents 6b847a59d908
children d8d6d01505ed
rev   line source
Chris@152 1 /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
Chris@152 2
Chris@152 3 /*
Chris@152 4 Sonic Visualiser
Chris@152 5 An audio file viewer and annotation editor.
Chris@152 6 Centre for Digital Music, Queen Mary, University of London.
Chris@152 7 This file copyright 2006 Chris Cannam.
Chris@152 8
Chris@152 9 This program is free software; you can redistribute it and/or
Chris@152 10 modify it under the terms of the GNU General Public License as
Chris@152 11 published by the Free Software Foundation; either version 2 of the
Chris@152 12 License, or (at your option) any later version. See the file
Chris@152 13 COPYING included with this distribution for more information.
Chris@152 14 */
Chris@152 15
Chris@152 16 #include "FFTModel.h"
Chris@152 17 #include "DenseTimeValueModel.h"
Chris@152 18
Chris@183 19 #include "base/Profiler.h"
Chris@275 20 #include "base/Pitch.h"
Chris@183 21
Chris@402 22 #include <algorithm>
Chris@402 23
Chris@152 24 #include <cassert>
Chris@1090 25 #include <deque>
Chris@152 26
Chris@1090 27 using namespace std;
Chris@1090 28
Chris@152 29 FFTModel::FFTModel(const DenseTimeValueModel *model,
Chris@152 30 int channel,
Chris@152 31 WindowType windowType,
Chris@929 32 int windowSize,
Chris@929 33 int windowIncrement,
Chris@1090 34 int fftSize) :
Chris@1090 35 m_model(model),
Chris@1090 36 m_channel(channel),
Chris@1090 37 m_windowType(windowType),
Chris@1090 38 m_windowSize(windowSize),
Chris@1090 39 m_windowIncrement(windowIncrement),
Chris@1090 40 m_fftSize(fftSize),
Chris@1091 41 m_windower(windowType, windowSize),
Chris@1093 42 m_fft(fftSize),
Chris@1093 43 m_cacheSize(3)
Chris@152 44 {
Chris@1091 45 if (m_windowSize > m_fftSize) {
Chris@1091 46 cerr << "ERROR: FFTModel::FFTModel: window size (" << m_windowSize
Chris@1091 47 << ") must be at least FFT size (" << m_fftSize << ")" << endl;
Chris@1091 48 throw invalid_argument("FFTModel window size must be at least FFT size");
Chris@1091 49 }
Chris@1133 50
Chris@1133 51 connect(model, SIGNAL(modelChanged()), this, SIGNAL(modelChanged()));
Chris@1133 52 connect(model, SIGNAL(modelChangedWithin(sv_frame_t, sv_frame_t)),
Chris@1133 53 this, SIGNAL(modelChangedWithin(sv_frame_t, sv_frame_t)));
Chris@152 54 }
Chris@152 55
Chris@152 56 FFTModel::~FFTModel()
Chris@152 57 {
Chris@152 58 }
Chris@152 59
Chris@360 60 void
Chris@360 61 FFTModel::sourceModelAboutToBeDeleted()
Chris@360 62 {
Chris@1090 63 if (m_model) {
Chris@1090 64 cerr << "FFTModel[" << this << "]::sourceModelAboutToBeDeleted(" << m_model << ")" << endl;
Chris@1090 65 m_model = 0;
Chris@360 66 }
Chris@360 67 }
Chris@360 68
Chris@1091 69 int
Chris@1091 70 FFTModel::getWidth() const
Chris@1091 71 {
Chris@1091 72 if (!m_model) return 0;
Chris@1091 73 return int((m_model->getEndFrame() - m_model->getStartFrame())
Chris@1091 74 / m_windowIncrement) + 1;
Chris@1091 75 }
Chris@1091 76
Chris@1091 77 int
Chris@1091 78 FFTModel::getHeight() const
Chris@1091 79 {
Chris@1091 80 return m_fftSize / 2 + 1;
Chris@1091 81 }
Chris@1091 82
Chris@152 83 QString
Chris@929 84 FFTModel::getBinName(int n) const
Chris@152 85 {
Chris@1040 86 sv_samplerate_t sr = getSampleRate();
Chris@152 87 if (!sr) return "";
Chris@204 88 QString name = tr("%1 Hz").arg((n * sr) / ((getHeight()-1) * 2));
Chris@152 89 return name;
Chris@152 90 }
Chris@152 91
Chris@1091 92 FFTModel::Column
Chris@1091 93 FFTModel::getColumn(int x) const
Chris@1091 94 {
Chris@1091 95 auto cplx = getFFTColumn(x);
Chris@1091 96 Column col;
Chris@1154 97 col.reserve(cplx.size());
Chris@1091 98 for (auto c: cplx) col.push_back(abs(c));
Chris@1154 99 return move(col);
Chris@1091 100 }
Chris@1091 101
Chris@1200 102 FFTModel::Column
Chris@1200 103 FFTModel::getPhases(int x) const
Chris@1200 104 {
Chris@1200 105 auto cplx = getFFTColumn(x);
Chris@1200 106 Column col;
Chris@1200 107 col.reserve(cplx.size());
Chris@1201 108 for (auto c: cplx) {
Chris@1201 109 col.push_back(arg(c));
Chris@1201 110 }
Chris@1200 111 return move(col);
Chris@1200 112 }
Chris@1200 113
Chris@1091 114 float
Chris@1091 115 FFTModel::getMagnitudeAt(int x, int y) const
Chris@1091 116 {
Chris@1093 117 if (x < 0 || x >= getWidth() || y < 0 || y >= getHeight()) return 0.f;
Chris@1093 118 auto col = getFFTColumn(x);
Chris@1093 119 return abs(col[y]);
Chris@1091 120 }
Chris@1091 121
Chris@1091 122 float
Chris@1091 123 FFTModel::getMaximumMagnitudeAt(int x) const
Chris@1091 124 {
Chris@1091 125 Column col(getColumn(x));
Chris@1092 126 float max = 0.f;
Chris@1154 127 int n = int(col.size());
Chris@1154 128 for (int i = 0; i < n; ++i) {
Chris@1092 129 if (col[i] > max) max = col[i];
Chris@1092 130 }
Chris@1092 131 return max;
Chris@1091 132 }
Chris@1091 133
Chris@1091 134 float
Chris@1091 135 FFTModel::getPhaseAt(int x, int y) const
Chris@1091 136 {
Chris@1093 137 if (x < 0 || x >= getWidth() || y < 0 || y >= getHeight()) return 0.f;
Chris@1091 138 return arg(getFFTColumn(x)[y]);
Chris@1091 139 }
Chris@1091 140
Chris@1091 141 void
Chris@1091 142 FFTModel::getValuesAt(int x, int y, float &re, float &im) const
Chris@1091 143 {
Chris@1091 144 auto col = getFFTColumn(x);
Chris@1091 145 re = col[y].real();
Chris@1091 146 im = col[y].imag();
Chris@1091 147 }
Chris@1091 148
Chris@1091 149 bool
Chris@1091 150 FFTModel::getMagnitudesAt(int x, float *values, int minbin, int count) const
Chris@1091 151 {
Chris@1091 152 if (count == 0) count = getHeight();
Chris@1091 153 auto col = getFFTColumn(x);
Chris@1091 154 for (int i = 0; i < count; ++i) {
Chris@1091 155 values[i] = abs(col[minbin + i]);
Chris@1091 156 }
Chris@1091 157 return true;
Chris@1091 158 }
Chris@1091 159
Chris@1091 160 bool
Chris@1091 161 FFTModel::getPhasesAt(int x, float *values, int minbin, int count) const
Chris@1091 162 {
Chris@1091 163 if (count == 0) count = getHeight();
Chris@1091 164 auto col = getFFTColumn(x);
Chris@1091 165 for (int i = 0; i < count; ++i) {
Chris@1091 166 values[i] = arg(col[minbin + i]);
Chris@1091 167 }
Chris@1091 168 return true;
Chris@1091 169 }
Chris@1091 170
Chris@1091 171 bool
Chris@1091 172 FFTModel::getValuesAt(int x, float *reals, float *imags, int minbin, int count) const
Chris@1091 173 {
Chris@1091 174 if (count == 0) count = getHeight();
Chris@1091 175 auto col = getFFTColumn(x);
Chris@1091 176 for (int i = 0; i < count; ++i) {
Chris@1091 177 reals[i] = col[minbin + i].real();
Chris@1091 178 }
Chris@1091 179 for (int i = 0; i < count; ++i) {
Chris@1091 180 imags[i] = col[minbin + i].imag();
Chris@1091 181 }
Chris@1091 182 return true;
Chris@1091 183 }
Chris@1091 184
Chris@1091 185 vector<float>
Chris@1091 186 FFTModel::getSourceSamples(int column) const
Chris@1091 187 {
Chris@1094 188 // m_fftSize may be greater than m_windowSize, but not the reverse
Chris@1094 189
Chris@1094 190 // cerr << "getSourceSamples(" << column << ")" << endl;
Chris@1094 191
Chris@1091 192 auto range = getSourceSampleRange(column);
Chris@1094 193 auto data = getSourceData(range);
Chris@1094 194
Chris@1091 195 int off = (m_fftSize - m_windowSize) / 2;
Chris@1094 196
Chris@1094 197 if (off == 0) {
Chris@1094 198 return data;
Chris@1094 199 } else {
Chris@1094 200 vector<float> pad(off, 0.f);
Chris@1094 201 vector<float> padded;
Chris@1094 202 padded.reserve(m_fftSize);
Chris@1094 203 padded.insert(padded.end(), pad.begin(), pad.end());
Chris@1094 204 padded.insert(padded.end(), data.begin(), data.end());
Chris@1094 205 padded.insert(padded.end(), pad.begin(), pad.end());
Chris@1094 206 return padded;
Chris@1094 207 }
Chris@1094 208 }
Chris@1094 209
Chris@1094 210 vector<float>
Chris@1094 211 FFTModel::getSourceData(pair<sv_frame_t, sv_frame_t> range) const
Chris@1094 212 {
Chris@1094 213 // cerr << "getSourceData(" << range.first << "," << range.second
Chris@1094 214 // << "): saved range is (" << m_savedData.range.first
Chris@1094 215 // << "," << m_savedData.range.second << ")" << endl;
Chris@1094 216
Chris@1100 217 if (m_savedData.range == range) {
Chris@1100 218 return m_savedData.data;
Chris@1100 219 }
Chris@1094 220
Chris@1094 221 if (range.first < m_savedData.range.second &&
Chris@1094 222 range.first >= m_savedData.range.first &&
Chris@1094 223 range.second > m_savedData.range.second) {
Chris@1094 224
Chris@1100 225 sv_frame_t discard = range.first - m_savedData.range.first;
Chris@1100 226
Chris@1100 227 vector<float> acc(m_savedData.data.begin() + discard,
Chris@1100 228 m_savedData.data.end());
Chris@1094 229
Chris@1095 230 vector<float> rest =
Chris@1095 231 getSourceDataUncached({ m_savedData.range.second, range.second });
Chris@1100 232
Chris@1100 233 acc.insert(acc.end(), rest.begin(), rest.end());
Chris@1094 234
Chris@1095 235 m_savedData = { range, acc };
Chris@1095 236 return acc;
Chris@1095 237
Chris@1095 238 } else {
Chris@1095 239
Chris@1095 240 auto data = getSourceDataUncached(range);
Chris@1095 241 m_savedData = { range, data };
Chris@1095 242 return data;
Chris@1094 243 }
Chris@1095 244 }
Chris@1094 245
Chris@1095 246 vector<float>
Chris@1095 247 FFTModel::getSourceDataUncached(pair<sv_frame_t, sv_frame_t> range) const
Chris@1095 248 {
Chris@1091 249 decltype(range.first) pfx = 0;
Chris@1091 250 if (range.first < 0) {
Chris@1091 251 pfx = -range.first;
Chris@1091 252 range = { 0, range.second };
Chris@1091 253 }
Chris@1096 254
Chris@1096 255 auto data = m_model->getData(m_channel,
Chris@1096 256 range.first,
Chris@1096 257 range.second - range.first);
Chris@1096 258
Chris@1096 259 // don't return a partial frame
Chris@1096 260 data.resize(range.second - range.first, 0.f);
Chris@1096 261
Chris@1096 262 if (pfx > 0) {
Chris@1096 263 vector<float> pad(pfx, 0.f);
Chris@1096 264 data.insert(data.begin(), pad.begin(), pad.end());
Chris@1096 265 }
Chris@1096 266
Chris@1091 267 if (m_channel == -1) {
Chris@1091 268 int channels = m_model->getChannelCount();
Chris@1091 269 if (channels > 1) {
Chris@1096 270 int n = int(data.size());
Chris@1096 271 float factor = 1.f / float(channels);
Chris@1100 272 // use mean instead of sum for fft model input
Chris@1096 273 for (int i = 0; i < n; ++i) {
Chris@1096 274 data[i] *= factor;
Chris@1091 275 }
Chris@1091 276 }
Chris@1091 277 }
Chris@1094 278
Chris@1094 279 return data;
Chris@1091 280 }
Chris@1091 281
Chris@1091 282 vector<complex<float>>
Chris@1093 283 FFTModel::getFFTColumn(int n) const
Chris@1091 284 {
Chris@1093 285 for (auto &incache : m_cached) {
Chris@1093 286 if (incache.n == n) {
Chris@1093 287 return incache.col;
Chris@1093 288 }
Chris@1093 289 }
Chris@1093 290
Chris@1093 291 auto samples = getSourceSamples(n);
Chris@1100 292 m_windower.cut(samples.data());
Chris@1093 293 auto col = m_fft.process(samples);
Chris@1093 294
Chris@1093 295 SavedColumn sc { n, col };
Chris@1093 296 if (m_cached.size() >= m_cacheSize) {
Chris@1093 297 m_cached.pop_front();
Chris@1093 298 }
Chris@1093 299 m_cached.push_back(sc);
Chris@1093 300
Chris@1154 301 return move(col);
Chris@1091 302 }
Chris@1091 303
Chris@275 304 bool
Chris@1045 305 FFTModel::estimateStableFrequency(int x, int y, double &frequency)
Chris@275 306 {
Chris@275 307 if (!isOK()) return false;
Chris@275 308
Chris@1090 309 frequency = double(y * getSampleRate()) / m_fftSize;
Chris@275 310
Chris@275 311 if (x+1 >= getWidth()) return false;
Chris@275 312
Chris@275 313 // At frequency f, a phase shift of 2pi (one cycle) happens in 1/f sec.
Chris@275 314 // At hopsize h and sample rate sr, one hop happens in h/sr sec.
Chris@275 315 // At window size w, for bin b, f is b*sr/w.
Chris@275 316 // thus 2pi phase shift happens in w/(b*sr) sec.
Chris@275 317 // We need to know what phase shift we expect from h/sr sec.
Chris@275 318 // -> 2pi * ((h/sr) / (w/(b*sr)))
Chris@275 319 // = 2pi * ((h * b * sr) / (w * sr))
Chris@275 320 // = 2pi * (h * b) / w.
Chris@275 321
Chris@1038 322 double oldPhase = getPhaseAt(x, y);
Chris@1038 323 double newPhase = getPhaseAt(x+1, y);
Chris@275 324
Chris@929 325 int incr = getResolution();
Chris@275 326
Chris@1090 327 double expectedPhase = oldPhase + (2.0 * M_PI * y * incr) / m_fftSize;
Chris@275 328
Chris@1038 329 double phaseError = princarg(newPhase - expectedPhase);
Chris@275 330
Chris@275 331 // The new frequency estimate based on the phase error resulting
Chris@275 332 // from assuming the "native" frequency of this bin
Chris@275 333
Chris@275 334 frequency =
Chris@1090 335 (getSampleRate() * (expectedPhase + phaseError - oldPhase)) /
Chris@1045 336 (2.0 * M_PI * incr);
Chris@275 337
Chris@275 338 return true;
Chris@275 339 }
Chris@275 340
Chris@275 341 FFTModel::PeakLocationSet
Chris@1191 342 FFTModel::getPeaks(PeakPickType type, int x, int ymin, int ymax) const
Chris@275 343 {
Chris@551 344 Profiler profiler("FFTModel::getPeaks");
Chris@551 345
Chris@275 346 FFTModel::PeakLocationSet peaks;
Chris@275 347 if (!isOK()) return peaks;
Chris@275 348
Chris@275 349 if (ymax == 0 || ymax > getHeight() - 1) {
Chris@275 350 ymax = getHeight() - 1;
Chris@275 351 }
Chris@275 352
Chris@275 353 if (type == AllPeaks) {
Chris@551 354 int minbin = ymin;
Chris@551 355 if (minbin > 0) minbin = minbin - 1;
Chris@551 356 int maxbin = ymax;
Chris@551 357 if (maxbin < getHeight() - 1) maxbin = maxbin + 1;
Chris@551 358 const int n = maxbin - minbin + 1;
Chris@1218 359 float *values = new float[n];
Chris@551 360 getMagnitudesAt(x, values, minbin, maxbin - minbin + 1);
Chris@929 361 for (int bin = ymin; bin <= ymax; ++bin) {
Chris@551 362 if (bin == minbin || bin == maxbin) continue;
Chris@551 363 if (values[bin - minbin] > values[bin - minbin - 1] &&
Chris@551 364 values[bin - minbin] > values[bin - minbin + 1]) {
Chris@275 365 peaks.insert(bin);
Chris@275 366 }
Chris@275 367 }
Chris@1218 368 delete[] values;
Chris@275 369 return peaks;
Chris@275 370 }
Chris@275 371
Chris@551 372 Column values = getColumn(x);
Chris@1154 373 int nv = int(values.size());
Chris@275 374
Chris@500 375 float mean = 0.f;
Chris@1154 376 for (int i = 0; i < nv; ++i) mean += values[i];
Chris@1154 377 if (nv > 0) mean = mean / float(values.size());
Chris@1038 378
Chris@275 379 // For peak picking we use a moving median window, picking the
Chris@275 380 // highest value within each continuous region of values that
Chris@275 381 // exceed the median. For pitch adaptivity, we adjust the window
Chris@275 382 // size to a roughly constant pitch range (about four tones).
Chris@275 383
Chris@1040 384 sv_samplerate_t sampleRate = getSampleRate();
Chris@275 385
Chris@1090 386 deque<float> window;
Chris@1090 387 vector<int> inrange;
Chris@280 388 float dist = 0.5;
Chris@500 389
Chris@929 390 int medianWinSize = getPeakPickWindowSize(type, sampleRate, ymin, dist);
Chris@929 391 int halfWin = medianWinSize/2;
Chris@275 392
Chris@929 393 int binmin;
Chris@275 394 if (ymin > halfWin) binmin = ymin - halfWin;
Chris@275 395 else binmin = 0;
Chris@275 396
Chris@929 397 int binmax;
Chris@1154 398 if (ymax + halfWin < nv) binmax = ymax + halfWin;
Chris@1154 399 else binmax = nv - 1;
Chris@275 400
Chris@929 401 int prevcentre = 0;
Chris@500 402
Chris@929 403 for (int bin = binmin; bin <= binmax; ++bin) {
Chris@275 404
Chris@275 405 float value = values[bin];
Chris@275 406
Chris@275 407 window.push_back(value);
Chris@275 408
Chris@280 409 // so-called median will actually be the dist*100'th percentile
Chris@280 410 medianWinSize = getPeakPickWindowSize(type, sampleRate, bin, dist);
Chris@275 411 halfWin = medianWinSize/2;
Chris@275 412
Chris@929 413 while ((int)window.size() > medianWinSize) {
Chris@500 414 window.pop_front();
Chris@500 415 }
Chris@500 416
Chris@1038 417 int actualSize = int(window.size());
Chris@275 418
Chris@275 419 if (type == MajorPitchAdaptivePeaks) {
Chris@1154 420 if (ymax + halfWin < nv) binmax = ymax + halfWin;
Chris@1154 421 else binmax = nv - 1;
Chris@275 422 }
Chris@275 423
Chris@1090 424 deque<float> sorted(window);
Chris@1090 425 sort(sorted.begin(), sorted.end());
Chris@1038 426 float median = sorted[int(float(sorted.size()) * dist)];
Chris@275 427
Chris@929 428 int centrebin = 0;
Chris@500 429 if (bin > actualSize/2) centrebin = bin - actualSize/2;
Chris@500 430
Chris@500 431 while (centrebin > prevcentre || bin == binmin) {
Chris@275 432
Chris@500 433 if (centrebin > prevcentre) ++prevcentre;
Chris@500 434
Chris@500 435 float centre = values[prevcentre];
Chris@500 436
Chris@500 437 if (centre > median) {
Chris@500 438 inrange.push_back(centrebin);
Chris@500 439 }
Chris@500 440
Chris@1154 441 if (centre <= median || centrebin+1 == nv) {
Chris@500 442 if (!inrange.empty()) {
Chris@929 443 int peakbin = 0;
Chris@500 444 float peakval = 0.f;
Chris@929 445 for (int i = 0; i < (int)inrange.size(); ++i) {
Chris@500 446 if (i == 0 || values[inrange[i]] > peakval) {
Chris@500 447 peakval = values[inrange[i]];
Chris@500 448 peakbin = inrange[i];
Chris@500 449 }
Chris@500 450 }
Chris@500 451 inrange.clear();
Chris@500 452 if (peakbin >= ymin && peakbin <= ymax) {
Chris@500 453 peaks.insert(peakbin);
Chris@275 454 }
Chris@275 455 }
Chris@275 456 }
Chris@500 457
Chris@500 458 if (bin == binmin) break;
Chris@275 459 }
Chris@275 460 }
Chris@275 461
Chris@275 462 return peaks;
Chris@275 463 }
Chris@275 464
Chris@929 465 int
Chris@1040 466 FFTModel::getPeakPickWindowSize(PeakPickType type, sv_samplerate_t sampleRate,
Chris@929 467 int bin, float &percentile) const
Chris@275 468 {
Chris@280 469 percentile = 0.5;
Chris@275 470 if (type == MajorPeaks) return 10;
Chris@275 471 if (bin == 0) return 3;
Chris@280 472
Chris@1091 473 double binfreq = (sampleRate * bin) / m_fftSize;
Chris@1038 474 double hifreq = Pitch::getFrequencyForPitch(73, 0, binfreq);
Chris@280 475
Chris@1091 476 int hibin = int(lrint((hifreq * m_fftSize) / sampleRate));
Chris@275 477 int medianWinSize = hibin - bin;
Chris@275 478 if (medianWinSize < 3) medianWinSize = 3;
Chris@280 479
Chris@1091 480 percentile = 0.5f + float(binfreq / sampleRate);
Chris@280 481
Chris@275 482 return medianWinSize;
Chris@275 483 }
Chris@275 484
Chris@275 485 FFTModel::PeakSet
Chris@929 486 FFTModel::getPeakFrequencies(PeakPickType type, int x,
Chris@1191 487 int ymin, int ymax) const
Chris@275 488 {
Chris@551 489 Profiler profiler("FFTModel::getPeakFrequencies");
Chris@551 490
Chris@275 491 PeakSet peaks;
Chris@275 492 if (!isOK()) return peaks;
Chris@275 493 PeakLocationSet locations = getPeaks(type, x, ymin, ymax);
Chris@275 494
Chris@1040 495 sv_samplerate_t sampleRate = getSampleRate();
Chris@929 496 int incr = getResolution();
Chris@275 497
Chris@275 498 // This duplicates some of the work of estimateStableFrequency to
Chris@275 499 // allow us to retrieve the phases in two separate vertical
Chris@275 500 // columns, instead of jumping back and forth between columns x and
Chris@275 501 // x+1, which may be significantly slower if re-seeking is needed
Chris@275 502
Chris@1090 503 vector<float> phases;
Chris@275 504 for (PeakLocationSet::iterator i = locations.begin();
Chris@275 505 i != locations.end(); ++i) {
Chris@275 506 phases.push_back(getPhaseAt(x, *i));
Chris@275 507 }
Chris@275 508
Chris@929 509 int phaseIndex = 0;
Chris@275 510 for (PeakLocationSet::iterator i = locations.begin();
Chris@275 511 i != locations.end(); ++i) {
Chris@1038 512 double oldPhase = phases[phaseIndex];
Chris@1038 513 double newPhase = getPhaseAt(x+1, *i);
Chris@1090 514 double expectedPhase = oldPhase + (2.0 * M_PI * *i * incr) / m_fftSize;
Chris@1038 515 double phaseError = princarg(newPhase - expectedPhase);
Chris@1038 516 double frequency =
Chris@275 517 (sampleRate * (expectedPhase + phaseError - oldPhase))
Chris@275 518 / (2 * M_PI * incr);
Chris@1045 519 peaks[*i] = frequency;
Chris@275 520 ++phaseIndex;
Chris@275 521 }
Chris@275 522
Chris@275 523 return peaks;
Chris@275 524 }
Chris@275 525