annotate data/model/FFTModel.cpp @ 1095:b66734b5f806 simple-fft-model

Fix to fft cache
author Chris Cannam
date Sat, 13 Jun 2015 08:47:05 +0100
parents b386363ff6c8
children 4d9816ba0ebe
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@608 27 #ifndef __GNUC__
Chris@608 28 #include <alloca.h>
Chris@608 29 #endif
Chris@608 30
Chris@1090 31 using namespace std;
Chris@1090 32
Chris@152 33 FFTModel::FFTModel(const DenseTimeValueModel *model,
Chris@152 34 int channel,
Chris@152 35 WindowType windowType,
Chris@929 36 int windowSize,
Chris@929 37 int windowIncrement,
Chris@1090 38 int fftSize) :
Chris@1090 39 m_model(model),
Chris@1090 40 m_channel(channel),
Chris@1090 41 m_windowType(windowType),
Chris@1090 42 m_windowSize(windowSize),
Chris@1090 43 m_windowIncrement(windowIncrement),
Chris@1090 44 m_fftSize(fftSize),
Chris@1091 45 m_windower(windowType, windowSize),
Chris@1093 46 m_fft(fftSize),
Chris@1093 47 m_cacheSize(3)
Chris@152 48 {
Chris@1091 49 if (m_windowSize > m_fftSize) {
Chris@1091 50 cerr << "ERROR: FFTModel::FFTModel: window size (" << m_windowSize
Chris@1091 51 << ") must be at least FFT size (" << m_fftSize << ")" << endl;
Chris@1091 52 throw invalid_argument("FFTModel window size must be at least FFT size");
Chris@1091 53 }
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@1091 97 col.reserve(int(cplx.size()));
Chris@1091 98 for (auto c: cplx) col.push_back(abs(c));
Chris@1091 99 return col;
Chris@1091 100 }
Chris@1091 101
Chris@1091 102 float
Chris@1091 103 FFTModel::getMagnitudeAt(int x, int y) const
Chris@1091 104 {
Chris@1093 105 if (x < 0 || x >= getWidth() || y < 0 || y >= getHeight()) return 0.f;
Chris@1093 106 auto col = getFFTColumn(x);
Chris@1093 107 return abs(col[y]);
Chris@1091 108 }
Chris@1091 109
Chris@1091 110 float
Chris@1091 111 FFTModel::getMaximumMagnitudeAt(int x) const
Chris@1091 112 {
Chris@1091 113 Column col(getColumn(x));
Chris@1092 114 float max = 0.f;
Chris@1092 115 for (int i = 0; i < col.size(); ++i) {
Chris@1092 116 if (col[i] > max) max = col[i];
Chris@1092 117 }
Chris@1092 118 return max;
Chris@1091 119 }
Chris@1091 120
Chris@1091 121 float
Chris@1091 122 FFTModel::getPhaseAt(int x, int y) const
Chris@1091 123 {
Chris@1093 124 if (x < 0 || x >= getWidth() || y < 0 || y >= getHeight()) return 0.f;
Chris@1091 125 return arg(getFFTColumn(x)[y]);
Chris@1091 126 }
Chris@1091 127
Chris@1091 128 void
Chris@1091 129 FFTModel::getValuesAt(int x, int y, float &re, float &im) const
Chris@1091 130 {
Chris@1091 131 auto col = getFFTColumn(x);
Chris@1091 132 re = col[y].real();
Chris@1091 133 im = col[y].imag();
Chris@1091 134 }
Chris@1091 135
Chris@1091 136 bool
Chris@1093 137 FFTModel::isColumnAvailable(int) const
Chris@1091 138 {
Chris@1091 139 //!!!
Chris@1091 140 return true;
Chris@1091 141 }
Chris@1091 142
Chris@1091 143 bool
Chris@1091 144 FFTModel::getMagnitudesAt(int x, float *values, int minbin, int count) const
Chris@1091 145 {
Chris@1091 146 if (count == 0) count = getHeight();
Chris@1091 147 auto col = getFFTColumn(x);
Chris@1091 148 for (int i = 0; i < count; ++i) {
Chris@1091 149 values[i] = abs(col[minbin + i]);
Chris@1091 150 }
Chris@1091 151 return true;
Chris@1091 152 }
Chris@1091 153
Chris@1091 154 bool
Chris@1091 155 FFTModel::getNormalizedMagnitudesAt(int x, float *values, int minbin, int count) const
Chris@1091 156 {
Chris@1092 157 if (!getMagnitudesAt(x, values, minbin, count)) return false;
Chris@1092 158 if (count == 0) count = getHeight();
Chris@1092 159 float max = 0.f;
Chris@1092 160 for (int i = 0; i < count; ++i) {
Chris@1092 161 if (values[i] > max) max = values[i];
Chris@1092 162 }
Chris@1092 163 if (max > 0.f) {
Chris@1092 164 for (int i = 0; i < count; ++i) {
Chris@1092 165 values[i] /= max;
Chris@1092 166 }
Chris@1092 167 }
Chris@1092 168 return true;
Chris@1091 169 }
Chris@1091 170
Chris@1091 171 bool
Chris@1091 172 FFTModel::getPhasesAt(int x, float *values, 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 values[i] = arg(col[minbin + i]);
Chris@1091 178 }
Chris@1091 179 return true;
Chris@1091 180 }
Chris@1091 181
Chris@1091 182 bool
Chris@1091 183 FFTModel::getValuesAt(int x, float *reals, float *imags, int minbin, int count) const
Chris@1091 184 {
Chris@1091 185 if (count == 0) count = getHeight();
Chris@1091 186 auto col = getFFTColumn(x);
Chris@1091 187 for (int i = 0; i < count; ++i) {
Chris@1091 188 reals[i] = col[minbin + i].real();
Chris@1091 189 }
Chris@1091 190 for (int i = 0; i < count; ++i) {
Chris@1091 191 imags[i] = col[minbin + i].imag();
Chris@1091 192 }
Chris@1091 193 return true;
Chris@1091 194 }
Chris@1091 195
Chris@1091 196 vector<float>
Chris@1091 197 FFTModel::getSourceSamples(int column) const
Chris@1091 198 {
Chris@1094 199 // m_fftSize may be greater than m_windowSize, but not the reverse
Chris@1094 200
Chris@1094 201 // cerr << "getSourceSamples(" << column << ")" << endl;
Chris@1094 202
Chris@1091 203 auto range = getSourceSampleRange(column);
Chris@1094 204 auto data = getSourceData(range);
Chris@1094 205
Chris@1091 206 int off = (m_fftSize - m_windowSize) / 2;
Chris@1094 207
Chris@1094 208 if (off == 0) {
Chris@1094 209 return data;
Chris@1094 210 } else {
Chris@1094 211 vector<float> pad(off, 0.f);
Chris@1094 212 vector<float> padded;
Chris@1094 213 padded.reserve(m_fftSize);
Chris@1094 214 padded.insert(padded.end(), pad.begin(), pad.end());
Chris@1094 215 padded.insert(padded.end(), data.begin(), data.end());
Chris@1094 216 padded.insert(padded.end(), pad.begin(), pad.end());
Chris@1094 217 return padded;
Chris@1094 218 }
Chris@1094 219 }
Chris@1094 220
Chris@1094 221 vector<float>
Chris@1094 222 FFTModel::getSourceData(pair<sv_frame_t, sv_frame_t> range) const
Chris@1094 223 {
Chris@1094 224 // cerr << "getSourceData(" << range.first << "," << range.second
Chris@1094 225 // << "): saved range is (" << m_savedData.range.first
Chris@1094 226 // << "," << m_savedData.range.second << ")" << endl;
Chris@1094 227
Chris@1094 228 if (m_savedData.range == range) return m_savedData.data;
Chris@1094 229
Chris@1094 230 if (range.first < m_savedData.range.second &&
Chris@1094 231 range.first >= m_savedData.range.first &&
Chris@1094 232 range.second > m_savedData.range.second) {
Chris@1094 233
Chris@1094 234 //!!! Need FFTModel overlap tests to exercise this
Chris@1094 235
Chris@1094 236 sv_frame_t off = range.first - m_savedData.range.first;
Chris@1094 237
Chris@1095 238 vector<float> acc(m_savedData.data.begin() + off, m_savedData.data.end());
Chris@1094 239
Chris@1095 240 vector<float> rest =
Chris@1095 241 getSourceDataUncached({ m_savedData.range.second, range.second });
Chris@1094 242
Chris@1095 243 acc.insert(acc.end(), rest.begin(), rest.end());
Chris@1095 244
Chris@1095 245 m_savedData = { range, acc };
Chris@1095 246 return acc;
Chris@1095 247
Chris@1095 248 } else {
Chris@1095 249
Chris@1095 250 auto data = getSourceDataUncached(range);
Chris@1095 251 m_savedData = { range, data };
Chris@1095 252 return data;
Chris@1094 253 }
Chris@1095 254 }
Chris@1094 255
Chris@1095 256 vector<float>
Chris@1095 257 FFTModel::getSourceDataUncached(pair<sv_frame_t, sv_frame_t> range) const
Chris@1095 258 {
Chris@1094 259 vector<float> data(range.second - range.first, 0.f);
Chris@1091 260 decltype(range.first) pfx = 0;
Chris@1091 261 if (range.first < 0) {
Chris@1091 262 pfx = -range.first;
Chris@1091 263 range = { 0, range.second };
Chris@1091 264 }
Chris@1094 265 // cerr << "requesting " << range.second - range.first << " from file" << endl;
Chris@1091 266 (void) m_model->getData(m_channel,
Chris@1091 267 range.first,
Chris@1091 268 range.second - range.first,
Chris@1094 269 &data[pfx]);
Chris@1091 270 if (m_channel == -1) {
Chris@1091 271 int channels = m_model->getChannelCount();
Chris@1091 272 if (channels > 1) {
Chris@1094 273 for (int i = 0; in_range_for(data, i); ++i) {
Chris@1094 274 data[i] /= float(channels);
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@1091 292 m_windower.cut(&samples[0]);
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@1093 301 return 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@929 342 FFTModel::getPeaks(PeakPickType type, int x, int ymin, int ymax)
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@608 359 #ifdef __GNUC__
Chris@551 360 float values[n];
Chris@608 361 #else
Chris@608 362 float *values = (float *)alloca(n * sizeof(float));
Chris@608 363 #endif
Chris@551 364 getMagnitudesAt(x, values, minbin, maxbin - minbin + 1);
Chris@929 365 for (int bin = ymin; bin <= ymax; ++bin) {
Chris@551 366 if (bin == minbin || bin == maxbin) continue;
Chris@551 367 if (values[bin - minbin] > values[bin - minbin - 1] &&
Chris@551 368 values[bin - minbin] > values[bin - minbin + 1]) {
Chris@275 369 peaks.insert(bin);
Chris@275 370 }
Chris@275 371 }
Chris@275 372 return peaks;
Chris@275 373 }
Chris@275 374
Chris@551 375 Column values = getColumn(x);
Chris@275 376
Chris@500 377 float mean = 0.f;
Chris@551 378 for (int i = 0; i < values.size(); ++i) mean += values[i];
Chris@1038 379 if (values.size() > 0) mean = mean / float(values.size());
Chris@1038 380
Chris@275 381 // For peak picking we use a moving median window, picking the
Chris@275 382 // highest value within each continuous region of values that
Chris@275 383 // exceed the median. For pitch adaptivity, we adjust the window
Chris@275 384 // size to a roughly constant pitch range (about four tones).
Chris@275 385
Chris@1040 386 sv_samplerate_t sampleRate = getSampleRate();
Chris@275 387
Chris@1090 388 deque<float> window;
Chris@1090 389 vector<int> inrange;
Chris@280 390 float dist = 0.5;
Chris@500 391
Chris@929 392 int medianWinSize = getPeakPickWindowSize(type, sampleRate, ymin, dist);
Chris@929 393 int halfWin = medianWinSize/2;
Chris@275 394
Chris@929 395 int binmin;
Chris@275 396 if (ymin > halfWin) binmin = ymin - halfWin;
Chris@275 397 else binmin = 0;
Chris@275 398
Chris@929 399 int binmax;
Chris@275 400 if (ymax + halfWin < values.size()) binmax = ymax + halfWin;
Chris@275 401 else binmax = values.size()-1;
Chris@275 402
Chris@929 403 int prevcentre = 0;
Chris@500 404
Chris@929 405 for (int bin = binmin; bin <= binmax; ++bin) {
Chris@275 406
Chris@275 407 float value = values[bin];
Chris@275 408
Chris@275 409 window.push_back(value);
Chris@275 410
Chris@280 411 // so-called median will actually be the dist*100'th percentile
Chris@280 412 medianWinSize = getPeakPickWindowSize(type, sampleRate, bin, dist);
Chris@275 413 halfWin = medianWinSize/2;
Chris@275 414
Chris@929 415 while ((int)window.size() > medianWinSize) {
Chris@500 416 window.pop_front();
Chris@500 417 }
Chris@500 418
Chris@1038 419 int actualSize = int(window.size());
Chris@275 420
Chris@275 421 if (type == MajorPitchAdaptivePeaks) {
Chris@275 422 if (ymax + halfWin < values.size()) binmax = ymax + halfWin;
Chris@275 423 else binmax = values.size()-1;
Chris@275 424 }
Chris@275 425
Chris@1090 426 deque<float> sorted(window);
Chris@1090 427 sort(sorted.begin(), sorted.end());
Chris@1038 428 float median = sorted[int(float(sorted.size()) * dist)];
Chris@275 429
Chris@929 430 int centrebin = 0;
Chris@500 431 if (bin > actualSize/2) centrebin = bin - actualSize/2;
Chris@500 432
Chris@500 433 while (centrebin > prevcentre || bin == binmin) {
Chris@275 434
Chris@500 435 if (centrebin > prevcentre) ++prevcentre;
Chris@500 436
Chris@500 437 float centre = values[prevcentre];
Chris@500 438
Chris@500 439 if (centre > median) {
Chris@500 440 inrange.push_back(centrebin);
Chris@500 441 }
Chris@500 442
Chris@500 443 if (centre <= median || centrebin+1 == values.size()) {
Chris@500 444 if (!inrange.empty()) {
Chris@929 445 int peakbin = 0;
Chris@500 446 float peakval = 0.f;
Chris@929 447 for (int i = 0; i < (int)inrange.size(); ++i) {
Chris@500 448 if (i == 0 || values[inrange[i]] > peakval) {
Chris@500 449 peakval = values[inrange[i]];
Chris@500 450 peakbin = inrange[i];
Chris@500 451 }
Chris@500 452 }
Chris@500 453 inrange.clear();
Chris@500 454 if (peakbin >= ymin && peakbin <= ymax) {
Chris@500 455 peaks.insert(peakbin);
Chris@275 456 }
Chris@275 457 }
Chris@275 458 }
Chris@500 459
Chris@500 460 if (bin == binmin) break;
Chris@275 461 }
Chris@275 462 }
Chris@275 463
Chris@275 464 return peaks;
Chris@275 465 }
Chris@275 466
Chris@929 467 int
Chris@1040 468 FFTModel::getPeakPickWindowSize(PeakPickType type, sv_samplerate_t sampleRate,
Chris@929 469 int bin, float &percentile) const
Chris@275 470 {
Chris@280 471 percentile = 0.5;
Chris@275 472 if (type == MajorPeaks) return 10;
Chris@275 473 if (bin == 0) return 3;
Chris@280 474
Chris@1091 475 double binfreq = (sampleRate * bin) / m_fftSize;
Chris@1038 476 double hifreq = Pitch::getFrequencyForPitch(73, 0, binfreq);
Chris@280 477
Chris@1091 478 int hibin = int(lrint((hifreq * m_fftSize) / sampleRate));
Chris@275 479 int medianWinSize = hibin - bin;
Chris@275 480 if (medianWinSize < 3) medianWinSize = 3;
Chris@280 481
Chris@1091 482 percentile = 0.5f + float(binfreq / sampleRate);
Chris@280 483
Chris@275 484 return medianWinSize;
Chris@275 485 }
Chris@275 486
Chris@275 487 FFTModel::PeakSet
Chris@929 488 FFTModel::getPeakFrequencies(PeakPickType type, int x,
Chris@929 489 int ymin, int ymax)
Chris@275 490 {
Chris@551 491 Profiler profiler("FFTModel::getPeakFrequencies");
Chris@551 492
Chris@275 493 PeakSet peaks;
Chris@275 494 if (!isOK()) return peaks;
Chris@275 495 PeakLocationSet locations = getPeaks(type, x, ymin, ymax);
Chris@275 496
Chris@1040 497 sv_samplerate_t sampleRate = getSampleRate();
Chris@929 498 int incr = getResolution();
Chris@275 499
Chris@275 500 // This duplicates some of the work of estimateStableFrequency to
Chris@275 501 // allow us to retrieve the phases in two separate vertical
Chris@275 502 // columns, instead of jumping back and forth between columns x and
Chris@275 503 // x+1, which may be significantly slower if re-seeking is needed
Chris@275 504
Chris@1090 505 vector<float> phases;
Chris@275 506 for (PeakLocationSet::iterator i = locations.begin();
Chris@275 507 i != locations.end(); ++i) {
Chris@275 508 phases.push_back(getPhaseAt(x, *i));
Chris@275 509 }
Chris@275 510
Chris@929 511 int phaseIndex = 0;
Chris@275 512 for (PeakLocationSet::iterator i = locations.begin();
Chris@275 513 i != locations.end(); ++i) {
Chris@1038 514 double oldPhase = phases[phaseIndex];
Chris@1038 515 double newPhase = getPhaseAt(x+1, *i);
Chris@1090 516 double expectedPhase = oldPhase + (2.0 * M_PI * *i * incr) / m_fftSize;
Chris@1038 517 double phaseError = princarg(newPhase - expectedPhase);
Chris@1038 518 double frequency =
Chris@275 519 (sampleRate * (expectedPhase + phaseError - oldPhase))
Chris@275 520 / (2 * M_PI * incr);
Chris@1045 521 peaks[*i] = frequency;
Chris@275 522 ++phaseIndex;
Chris@275 523 }
Chris@275 524
Chris@275 525 return peaks;
Chris@275 526 }
Chris@275 527