annotate data/model/FFTModel.cpp @ 1186:12a8daa89970 spectrogram-minor-refactor

Mid-refactor to pull out the bulk of paintDrawBuffer into chunks
author Chris Cannam
date Mon, 13 Jun 2016 16:17:44 +0100
parents 444d133b5ab7
children 6d09ad2ab21f
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@1133 54
Chris@1133 55 connect(model, SIGNAL(modelChanged()), this, SIGNAL(modelChanged()));
Chris@1133 56 connect(model, SIGNAL(modelChangedWithin(sv_frame_t, sv_frame_t)),
Chris@1133 57 this, SIGNAL(modelChangedWithin(sv_frame_t, sv_frame_t)));
Chris@152 58 }
Chris@152 59
Chris@152 60 FFTModel::~FFTModel()
Chris@152 61 {
Chris@152 62 }
Chris@152 63
Chris@360 64 void
Chris@360 65 FFTModel::sourceModelAboutToBeDeleted()
Chris@360 66 {
Chris@1090 67 if (m_model) {
Chris@1090 68 cerr << "FFTModel[" << this << "]::sourceModelAboutToBeDeleted(" << m_model << ")" << endl;
Chris@1090 69 m_model = 0;
Chris@360 70 }
Chris@360 71 }
Chris@360 72
Chris@1091 73 int
Chris@1091 74 FFTModel::getWidth() const
Chris@1091 75 {
Chris@1091 76 if (!m_model) return 0;
Chris@1091 77 return int((m_model->getEndFrame() - m_model->getStartFrame())
Chris@1091 78 / m_windowIncrement) + 1;
Chris@1091 79 }
Chris@1091 80
Chris@1091 81 int
Chris@1091 82 FFTModel::getHeight() const
Chris@1091 83 {
Chris@1091 84 return m_fftSize / 2 + 1;
Chris@1091 85 }
Chris@1091 86
Chris@152 87 QString
Chris@929 88 FFTModel::getBinName(int n) const
Chris@152 89 {
Chris@1040 90 sv_samplerate_t sr = getSampleRate();
Chris@152 91 if (!sr) return "";
Chris@204 92 QString name = tr("%1 Hz").arg((n * sr) / ((getHeight()-1) * 2));
Chris@152 93 return name;
Chris@152 94 }
Chris@152 95
Chris@1091 96 FFTModel::Column
Chris@1091 97 FFTModel::getColumn(int x) const
Chris@1091 98 {
Chris@1091 99 auto cplx = getFFTColumn(x);
Chris@1091 100 Column col;
Chris@1154 101 col.reserve(cplx.size());
Chris@1091 102 for (auto c: cplx) col.push_back(abs(c));
Chris@1154 103 return move(col);
Chris@1091 104 }
Chris@1091 105
Chris@1091 106 float
Chris@1091 107 FFTModel::getMagnitudeAt(int x, int y) const
Chris@1091 108 {
Chris@1093 109 if (x < 0 || x >= getWidth() || y < 0 || y >= getHeight()) return 0.f;
Chris@1093 110 auto col = getFFTColumn(x);
Chris@1093 111 return abs(col[y]);
Chris@1091 112 }
Chris@1091 113
Chris@1091 114 float
Chris@1091 115 FFTModel::getMaximumMagnitudeAt(int x) const
Chris@1091 116 {
Chris@1091 117 Column col(getColumn(x));
Chris@1092 118 float max = 0.f;
Chris@1154 119 int n = int(col.size());
Chris@1154 120 for (int i = 0; i < n; ++i) {
Chris@1092 121 if (col[i] > max) max = col[i];
Chris@1092 122 }
Chris@1092 123 return max;
Chris@1091 124 }
Chris@1091 125
Chris@1091 126 float
Chris@1091 127 FFTModel::getPhaseAt(int x, int y) const
Chris@1091 128 {
Chris@1093 129 if (x < 0 || x >= getWidth() || y < 0 || y >= getHeight()) return 0.f;
Chris@1091 130 return arg(getFFTColumn(x)[y]);
Chris@1091 131 }
Chris@1091 132
Chris@1091 133 void
Chris@1091 134 FFTModel::getValuesAt(int x, int y, float &re, float &im) const
Chris@1091 135 {
Chris@1091 136 auto col = getFFTColumn(x);
Chris@1091 137 re = col[y].real();
Chris@1091 138 im = col[y].imag();
Chris@1091 139 }
Chris@1091 140
Chris@1091 141 bool
Chris@1091 142 FFTModel::getMagnitudesAt(int x, float *values, int minbin, int count) const
Chris@1091 143 {
Chris@1091 144 if (count == 0) count = getHeight();
Chris@1091 145 auto col = getFFTColumn(x);
Chris@1091 146 for (int i = 0; i < count; ++i) {
Chris@1091 147 values[i] = abs(col[minbin + i]);
Chris@1091 148 }
Chris@1091 149 return true;
Chris@1091 150 }
Chris@1091 151
Chris@1091 152 bool
Chris@1091 153 FFTModel::getPhasesAt(int x, float *values, int minbin, int count) const
Chris@1091 154 {
Chris@1091 155 if (count == 0) count = getHeight();
Chris@1091 156 auto col = getFFTColumn(x);
Chris@1091 157 for (int i = 0; i < count; ++i) {
Chris@1091 158 values[i] = arg(col[minbin + i]);
Chris@1091 159 }
Chris@1091 160 return true;
Chris@1091 161 }
Chris@1091 162
Chris@1091 163 bool
Chris@1091 164 FFTModel::getValuesAt(int x, float *reals, float *imags, int minbin, int count) const
Chris@1091 165 {
Chris@1091 166 if (count == 0) count = getHeight();
Chris@1091 167 auto col = getFFTColumn(x);
Chris@1091 168 for (int i = 0; i < count; ++i) {
Chris@1091 169 reals[i] = col[minbin + i].real();
Chris@1091 170 }
Chris@1091 171 for (int i = 0; i < count; ++i) {
Chris@1091 172 imags[i] = col[minbin + i].imag();
Chris@1091 173 }
Chris@1091 174 return true;
Chris@1091 175 }
Chris@1091 176
Chris@1091 177 vector<float>
Chris@1091 178 FFTModel::getSourceSamples(int column) const
Chris@1091 179 {
Chris@1094 180 // m_fftSize may be greater than m_windowSize, but not the reverse
Chris@1094 181
Chris@1094 182 // cerr << "getSourceSamples(" << column << ")" << endl;
Chris@1094 183
Chris@1091 184 auto range = getSourceSampleRange(column);
Chris@1094 185 auto data = getSourceData(range);
Chris@1094 186
Chris@1091 187 int off = (m_fftSize - m_windowSize) / 2;
Chris@1094 188
Chris@1094 189 if (off == 0) {
Chris@1094 190 return data;
Chris@1094 191 } else {
Chris@1094 192 vector<float> pad(off, 0.f);
Chris@1094 193 vector<float> padded;
Chris@1094 194 padded.reserve(m_fftSize);
Chris@1094 195 padded.insert(padded.end(), pad.begin(), pad.end());
Chris@1094 196 padded.insert(padded.end(), data.begin(), data.end());
Chris@1094 197 padded.insert(padded.end(), pad.begin(), pad.end());
Chris@1094 198 return padded;
Chris@1094 199 }
Chris@1094 200 }
Chris@1094 201
Chris@1094 202 vector<float>
Chris@1094 203 FFTModel::getSourceData(pair<sv_frame_t, sv_frame_t> range) const
Chris@1094 204 {
Chris@1094 205 // cerr << "getSourceData(" << range.first << "," << range.second
Chris@1094 206 // << "): saved range is (" << m_savedData.range.first
Chris@1094 207 // << "," << m_savedData.range.second << ")" << endl;
Chris@1094 208
Chris@1100 209 if (m_savedData.range == range) {
Chris@1100 210 return m_savedData.data;
Chris@1100 211 }
Chris@1094 212
Chris@1094 213 if (range.first < m_savedData.range.second &&
Chris@1094 214 range.first >= m_savedData.range.first &&
Chris@1094 215 range.second > m_savedData.range.second) {
Chris@1094 216
Chris@1100 217 sv_frame_t discard = range.first - m_savedData.range.first;
Chris@1100 218
Chris@1100 219 vector<float> acc(m_savedData.data.begin() + discard,
Chris@1100 220 m_savedData.data.end());
Chris@1094 221
Chris@1095 222 vector<float> rest =
Chris@1095 223 getSourceDataUncached({ m_savedData.range.second, range.second });
Chris@1100 224
Chris@1100 225 acc.insert(acc.end(), rest.begin(), rest.end());
Chris@1094 226
Chris@1095 227 m_savedData = { range, acc };
Chris@1095 228 return acc;
Chris@1095 229
Chris@1095 230 } else {
Chris@1095 231
Chris@1095 232 auto data = getSourceDataUncached(range);
Chris@1095 233 m_savedData = { range, data };
Chris@1095 234 return data;
Chris@1094 235 }
Chris@1095 236 }
Chris@1094 237
Chris@1095 238 vector<float>
Chris@1095 239 FFTModel::getSourceDataUncached(pair<sv_frame_t, sv_frame_t> range) const
Chris@1095 240 {
Chris@1091 241 decltype(range.first) pfx = 0;
Chris@1091 242 if (range.first < 0) {
Chris@1091 243 pfx = -range.first;
Chris@1091 244 range = { 0, range.second };
Chris@1091 245 }
Chris@1096 246
Chris@1096 247 auto data = m_model->getData(m_channel,
Chris@1096 248 range.first,
Chris@1096 249 range.second - range.first);
Chris@1096 250
Chris@1096 251 // don't return a partial frame
Chris@1096 252 data.resize(range.second - range.first, 0.f);
Chris@1096 253
Chris@1096 254 if (pfx > 0) {
Chris@1096 255 vector<float> pad(pfx, 0.f);
Chris@1096 256 data.insert(data.begin(), pad.begin(), pad.end());
Chris@1096 257 }
Chris@1096 258
Chris@1091 259 if (m_channel == -1) {
Chris@1091 260 int channels = m_model->getChannelCount();
Chris@1091 261 if (channels > 1) {
Chris@1096 262 int n = int(data.size());
Chris@1096 263 float factor = 1.f / float(channels);
Chris@1100 264 // use mean instead of sum for fft model input
Chris@1096 265 for (int i = 0; i < n; ++i) {
Chris@1096 266 data[i] *= factor;
Chris@1091 267 }
Chris@1091 268 }
Chris@1091 269 }
Chris@1094 270
Chris@1094 271 return data;
Chris@1091 272 }
Chris@1091 273
Chris@1091 274 vector<complex<float>>
Chris@1093 275 FFTModel::getFFTColumn(int n) const
Chris@1091 276 {
Chris@1093 277 for (auto &incache : m_cached) {
Chris@1093 278 if (incache.n == n) {
Chris@1093 279 return incache.col;
Chris@1093 280 }
Chris@1093 281 }
Chris@1093 282
Chris@1093 283 auto samples = getSourceSamples(n);
Chris@1100 284 m_windower.cut(samples.data());
Chris@1093 285 auto col = m_fft.process(samples);
Chris@1093 286
Chris@1093 287 SavedColumn sc { n, col };
Chris@1093 288 if (m_cached.size() >= m_cacheSize) {
Chris@1093 289 m_cached.pop_front();
Chris@1093 290 }
Chris@1093 291 m_cached.push_back(sc);
Chris@1093 292
Chris@1154 293 return move(col);
Chris@1091 294 }
Chris@1091 295
Chris@275 296 bool
Chris@1045 297 FFTModel::estimateStableFrequency(int x, int y, double &frequency)
Chris@275 298 {
Chris@275 299 if (!isOK()) return false;
Chris@275 300
Chris@1090 301 frequency = double(y * getSampleRate()) / m_fftSize;
Chris@275 302
Chris@275 303 if (x+1 >= getWidth()) return false;
Chris@275 304
Chris@275 305 // At frequency f, a phase shift of 2pi (one cycle) happens in 1/f sec.
Chris@275 306 // At hopsize h and sample rate sr, one hop happens in h/sr sec.
Chris@275 307 // At window size w, for bin b, f is b*sr/w.
Chris@275 308 // thus 2pi phase shift happens in w/(b*sr) sec.
Chris@275 309 // We need to know what phase shift we expect from h/sr sec.
Chris@275 310 // -> 2pi * ((h/sr) / (w/(b*sr)))
Chris@275 311 // = 2pi * ((h * b * sr) / (w * sr))
Chris@275 312 // = 2pi * (h * b) / w.
Chris@275 313
Chris@1038 314 double oldPhase = getPhaseAt(x, y);
Chris@1038 315 double newPhase = getPhaseAt(x+1, y);
Chris@275 316
Chris@929 317 int incr = getResolution();
Chris@275 318
Chris@1090 319 double expectedPhase = oldPhase + (2.0 * M_PI * y * incr) / m_fftSize;
Chris@275 320
Chris@1038 321 double phaseError = princarg(newPhase - expectedPhase);
Chris@275 322
Chris@275 323 // The new frequency estimate based on the phase error resulting
Chris@275 324 // from assuming the "native" frequency of this bin
Chris@275 325
Chris@275 326 frequency =
Chris@1090 327 (getSampleRate() * (expectedPhase + phaseError - oldPhase)) /
Chris@1045 328 (2.0 * M_PI * incr);
Chris@275 329
Chris@275 330 return true;
Chris@275 331 }
Chris@275 332
Chris@275 333 FFTModel::PeakLocationSet
Chris@929 334 FFTModel::getPeaks(PeakPickType type, int x, int ymin, int ymax)
Chris@275 335 {
Chris@551 336 Profiler profiler("FFTModel::getPeaks");
Chris@551 337
Chris@275 338 FFTModel::PeakLocationSet peaks;
Chris@275 339 if (!isOK()) return peaks;
Chris@275 340
Chris@275 341 if (ymax == 0 || ymax > getHeight() - 1) {
Chris@275 342 ymax = getHeight() - 1;
Chris@275 343 }
Chris@275 344
Chris@275 345 if (type == AllPeaks) {
Chris@551 346 int minbin = ymin;
Chris@551 347 if (minbin > 0) minbin = minbin - 1;
Chris@551 348 int maxbin = ymax;
Chris@551 349 if (maxbin < getHeight() - 1) maxbin = maxbin + 1;
Chris@551 350 const int n = maxbin - minbin + 1;
Chris@608 351 #ifdef __GNUC__
Chris@551 352 float values[n];
Chris@608 353 #else
Chris@608 354 float *values = (float *)alloca(n * sizeof(float));
Chris@608 355 #endif
Chris@551 356 getMagnitudesAt(x, values, minbin, maxbin - minbin + 1);
Chris@929 357 for (int bin = ymin; bin <= ymax; ++bin) {
Chris@551 358 if (bin == minbin || bin == maxbin) continue;
Chris@551 359 if (values[bin - minbin] > values[bin - minbin - 1] &&
Chris@551 360 values[bin - minbin] > values[bin - minbin + 1]) {
Chris@275 361 peaks.insert(bin);
Chris@275 362 }
Chris@275 363 }
Chris@275 364 return peaks;
Chris@275 365 }
Chris@275 366
Chris@551 367 Column values = getColumn(x);
Chris@1154 368 int nv = int(values.size());
Chris@275 369
Chris@500 370 float mean = 0.f;
Chris@1154 371 for (int i = 0; i < nv; ++i) mean += values[i];
Chris@1154 372 if (nv > 0) mean = mean / float(values.size());
Chris@1038 373
Chris@275 374 // For peak picking we use a moving median window, picking the
Chris@275 375 // highest value within each continuous region of values that
Chris@275 376 // exceed the median. For pitch adaptivity, we adjust the window
Chris@275 377 // size to a roughly constant pitch range (about four tones).
Chris@275 378
Chris@1040 379 sv_samplerate_t sampleRate = getSampleRate();
Chris@275 380
Chris@1090 381 deque<float> window;
Chris@1090 382 vector<int> inrange;
Chris@280 383 float dist = 0.5;
Chris@500 384
Chris@929 385 int medianWinSize = getPeakPickWindowSize(type, sampleRate, ymin, dist);
Chris@929 386 int halfWin = medianWinSize/2;
Chris@275 387
Chris@929 388 int binmin;
Chris@275 389 if (ymin > halfWin) binmin = ymin - halfWin;
Chris@275 390 else binmin = 0;
Chris@275 391
Chris@929 392 int binmax;
Chris@1154 393 if (ymax + halfWin < nv) binmax = ymax + halfWin;
Chris@1154 394 else binmax = nv - 1;
Chris@275 395
Chris@929 396 int prevcentre = 0;
Chris@500 397
Chris@929 398 for (int bin = binmin; bin <= binmax; ++bin) {
Chris@275 399
Chris@275 400 float value = values[bin];
Chris@275 401
Chris@275 402 window.push_back(value);
Chris@275 403
Chris@280 404 // so-called median will actually be the dist*100'th percentile
Chris@280 405 medianWinSize = getPeakPickWindowSize(type, sampleRate, bin, dist);
Chris@275 406 halfWin = medianWinSize/2;
Chris@275 407
Chris@929 408 while ((int)window.size() > medianWinSize) {
Chris@500 409 window.pop_front();
Chris@500 410 }
Chris@500 411
Chris@1038 412 int actualSize = int(window.size());
Chris@275 413
Chris@275 414 if (type == MajorPitchAdaptivePeaks) {
Chris@1154 415 if (ymax + halfWin < nv) binmax = ymax + halfWin;
Chris@1154 416 else binmax = nv - 1;
Chris@275 417 }
Chris@275 418
Chris@1090 419 deque<float> sorted(window);
Chris@1090 420 sort(sorted.begin(), sorted.end());
Chris@1038 421 float median = sorted[int(float(sorted.size()) * dist)];
Chris@275 422
Chris@929 423 int centrebin = 0;
Chris@500 424 if (bin > actualSize/2) centrebin = bin - actualSize/2;
Chris@500 425
Chris@500 426 while (centrebin > prevcentre || bin == binmin) {
Chris@275 427
Chris@500 428 if (centrebin > prevcentre) ++prevcentre;
Chris@500 429
Chris@500 430 float centre = values[prevcentre];
Chris@500 431
Chris@500 432 if (centre > median) {
Chris@500 433 inrange.push_back(centrebin);
Chris@500 434 }
Chris@500 435
Chris@1154 436 if (centre <= median || centrebin+1 == nv) {
Chris@500 437 if (!inrange.empty()) {
Chris@929 438 int peakbin = 0;
Chris@500 439 float peakval = 0.f;
Chris@929 440 for (int i = 0; i < (int)inrange.size(); ++i) {
Chris@500 441 if (i == 0 || values[inrange[i]] > peakval) {
Chris@500 442 peakval = values[inrange[i]];
Chris@500 443 peakbin = inrange[i];
Chris@500 444 }
Chris@500 445 }
Chris@500 446 inrange.clear();
Chris@500 447 if (peakbin >= ymin && peakbin <= ymax) {
Chris@500 448 peaks.insert(peakbin);
Chris@275 449 }
Chris@275 450 }
Chris@275 451 }
Chris@500 452
Chris@500 453 if (bin == binmin) break;
Chris@275 454 }
Chris@275 455 }
Chris@275 456
Chris@275 457 return peaks;
Chris@275 458 }
Chris@275 459
Chris@929 460 int
Chris@1040 461 FFTModel::getPeakPickWindowSize(PeakPickType type, sv_samplerate_t sampleRate,
Chris@929 462 int bin, float &percentile) const
Chris@275 463 {
Chris@280 464 percentile = 0.5;
Chris@275 465 if (type == MajorPeaks) return 10;
Chris@275 466 if (bin == 0) return 3;
Chris@280 467
Chris@1091 468 double binfreq = (sampleRate * bin) / m_fftSize;
Chris@1038 469 double hifreq = Pitch::getFrequencyForPitch(73, 0, binfreq);
Chris@280 470
Chris@1091 471 int hibin = int(lrint((hifreq * m_fftSize) / sampleRate));
Chris@275 472 int medianWinSize = hibin - bin;
Chris@275 473 if (medianWinSize < 3) medianWinSize = 3;
Chris@280 474
Chris@1091 475 percentile = 0.5f + float(binfreq / sampleRate);
Chris@280 476
Chris@275 477 return medianWinSize;
Chris@275 478 }
Chris@275 479
Chris@275 480 FFTModel::PeakSet
Chris@929 481 FFTModel::getPeakFrequencies(PeakPickType type, int x,
Chris@929 482 int ymin, int ymax)
Chris@275 483 {
Chris@551 484 Profiler profiler("FFTModel::getPeakFrequencies");
Chris@551 485
Chris@275 486 PeakSet peaks;
Chris@275 487 if (!isOK()) return peaks;
Chris@275 488 PeakLocationSet locations = getPeaks(type, x, ymin, ymax);
Chris@275 489
Chris@1040 490 sv_samplerate_t sampleRate = getSampleRate();
Chris@929 491 int incr = getResolution();
Chris@275 492
Chris@275 493 // This duplicates some of the work of estimateStableFrequency to
Chris@275 494 // allow us to retrieve the phases in two separate vertical
Chris@275 495 // columns, instead of jumping back and forth between columns x and
Chris@275 496 // x+1, which may be significantly slower if re-seeking is needed
Chris@275 497
Chris@1090 498 vector<float> phases;
Chris@275 499 for (PeakLocationSet::iterator i = locations.begin();
Chris@275 500 i != locations.end(); ++i) {
Chris@275 501 phases.push_back(getPhaseAt(x, *i));
Chris@275 502 }
Chris@275 503
Chris@929 504 int phaseIndex = 0;
Chris@275 505 for (PeakLocationSet::iterator i = locations.begin();
Chris@275 506 i != locations.end(); ++i) {
Chris@1038 507 double oldPhase = phases[phaseIndex];
Chris@1038 508 double newPhase = getPhaseAt(x+1, *i);
Chris@1090 509 double expectedPhase = oldPhase + (2.0 * M_PI * *i * incr) / m_fftSize;
Chris@1038 510 double phaseError = princarg(newPhase - expectedPhase);
Chris@1038 511 double frequency =
Chris@275 512 (sampleRate * (expectedPhase + phaseError - oldPhase))
Chris@275 513 / (2 * M_PI * incr);
Chris@1045 514 peaks[*i] = frequency;
Chris@275 515 ++phaseIndex;
Chris@275 516 }
Chris@275 517
Chris@275 518 return peaks;
Chris@275 519 }
Chris@275 520