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33 #include "modules/webaudio/PeriodicWave.h"
35 #include "platform/audio/FFTFrame.h"
36 #include "platform/audio/VectorMath.h"
37 #include "modules/webaudio/OscillatorNode.h"
40 const unsigned PeriodicWaveSize = 4096; // This must be a power of two.
41 const unsigned NumberOfRanges = 36; // There should be 3 * log2(PeriodicWaveSize) 1/3 octave ranges.
42 const float CentsPerRange = 1200 / 3; // 1/3 Octave.
46 using namespace VectorMath;
48 PassRefPtrWillBeRawPtr<PeriodicWave> PeriodicWave::create(float sampleRate, Float32Array* real, Float32Array* imag)
50 bool isGood = real && imag && real->length() == imag->length();
53 RefPtrWillBeRawPtr<PeriodicWave> periodicWave = adoptRefWillBeNoop(new PeriodicWave(sampleRate));
54 size_t numberOfComponents = real->length();
55 periodicWave->createBandLimitedTables(real->data(), imag->data(), numberOfComponents);
61 PassRefPtrWillBeRawPtr<PeriodicWave> PeriodicWave::createSine(float sampleRate)
63 RefPtrWillBeRawPtr<PeriodicWave> periodicWave = adoptRefWillBeNoop(new PeriodicWave(sampleRate));
64 periodicWave->generateBasicWaveform(OscillatorNode::SINE);
68 PassRefPtrWillBeRawPtr<PeriodicWave> PeriodicWave::createSquare(float sampleRate)
70 RefPtrWillBeRawPtr<PeriodicWave> periodicWave = adoptRefWillBeNoop(new PeriodicWave(sampleRate));
71 periodicWave->generateBasicWaveform(OscillatorNode::SQUARE);
75 PassRefPtrWillBeRawPtr<PeriodicWave> PeriodicWave::createSawtooth(float sampleRate)
77 RefPtrWillBeRawPtr<PeriodicWave> periodicWave = adoptRefWillBeNoop(new PeriodicWave(sampleRate));
78 periodicWave->generateBasicWaveform(OscillatorNode::SAWTOOTH);
82 PassRefPtrWillBeRawPtr<PeriodicWave> PeriodicWave::createTriangle(float sampleRate)
84 RefPtrWillBeRawPtr<PeriodicWave> periodicWave = adoptRefWillBeNoop(new PeriodicWave(sampleRate));
85 periodicWave->generateBasicWaveform(OscillatorNode::TRIANGLE);
89 PeriodicWave::PeriodicWave(float sampleRate)
90 : m_sampleRate(sampleRate)
91 , m_periodicWaveSize(PeriodicWaveSize)
92 , m_numberOfRanges(NumberOfRanges)
93 , m_centsPerRange(CentsPerRange)
95 ScriptWrappable::init(this);
96 float nyquist = 0.5 * m_sampleRate;
97 m_lowestFundamentalFrequency = nyquist / maxNumberOfPartials();
98 m_rateScale = m_periodicWaveSize / m_sampleRate;
101 void PeriodicWave::waveDataForFundamentalFrequency(float fundamentalFrequency, float* &lowerWaveData, float* &higherWaveData, float& tableInterpolationFactor)
103 // Negative frequencies are allowed, in which case we alias to the positive frequency.
104 fundamentalFrequency = fabsf(fundamentalFrequency);
106 // Calculate the pitch range.
107 float ratio = fundamentalFrequency > 0 ? fundamentalFrequency / m_lowestFundamentalFrequency : 0.5;
108 float centsAboveLowestFrequency = log2f(ratio) * 1200;
110 // Add one to round-up to the next range just in time to truncate partials before aliasing occurs.
111 float pitchRange = 1 + centsAboveLowestFrequency / m_centsPerRange;
113 pitchRange = std::max(pitchRange, 0.0f);
114 pitchRange = std::min(pitchRange, static_cast<float>(m_numberOfRanges - 1));
116 // The words "lower" and "higher" refer to the table data having the lower and higher numbers of partials.
117 // It's a little confusing since the range index gets larger the more partials we cull out.
118 // So the lower table data will have a larger range index.
119 unsigned rangeIndex1 = static_cast<unsigned>(pitchRange);
120 unsigned rangeIndex2 = rangeIndex1 < m_numberOfRanges - 1 ? rangeIndex1 + 1 : rangeIndex1;
122 lowerWaveData = m_bandLimitedTables[rangeIndex2]->data();
123 higherWaveData = m_bandLimitedTables[rangeIndex1]->data();
125 // Ranges from 0 -> 1 to interpolate between lower -> higher.
126 tableInterpolationFactor = pitchRange - rangeIndex1;
129 unsigned PeriodicWave::maxNumberOfPartials() const
131 return m_periodicWaveSize / 2;
134 unsigned PeriodicWave::numberOfPartialsForRange(unsigned rangeIndex) const
136 // Number of cents below nyquist where we cull partials.
137 float centsToCull = rangeIndex * m_centsPerRange;
139 // A value from 0 -> 1 representing what fraction of the partials to keep.
140 float cullingScale = pow(2, -centsToCull / 1200);
142 // The very top range will have all the partials culled.
143 unsigned numberOfPartials = cullingScale * maxNumberOfPartials();
145 return numberOfPartials;
148 // Convert into time-domain wave buffers.
149 // One table is created for each range for non-aliasing playback at different playback rates.
150 // Thus, higher ranges have more high-frequency partials culled out.
151 void PeriodicWave::createBandLimitedTables(const float* realData, const float* imagData, unsigned numberOfComponents)
153 float normalizationScale = 1;
155 unsigned fftSize = m_periodicWaveSize;
156 unsigned halfSize = fftSize / 2;
159 numberOfComponents = std::min(numberOfComponents, halfSize);
161 m_bandLimitedTables.reserveCapacity(m_numberOfRanges);
163 for (unsigned rangeIndex = 0; rangeIndex < m_numberOfRanges; ++rangeIndex) {
164 // This FFTFrame is used to cull partials (represented by frequency bins).
165 FFTFrame frame(fftSize);
166 float* realP = frame.realData();
167 float* imagP = frame.imagData();
169 // Copy from loaded frequency data and scale.
170 float scale = fftSize;
171 vsmul(realData, 1, &scale, realP, 1, numberOfComponents);
172 vsmul(imagData, 1, &scale, imagP, 1, numberOfComponents);
174 // If fewer components were provided than 1/2 FFT size, then clear the remaining bins.
175 for (i = numberOfComponents; i < halfSize; ++i) {
180 // Generate complex conjugate because of the way the inverse FFT is defined.
182 vsmul(imagP, 1, &minusOne, imagP, 1, halfSize);
184 // Find the starting bin where we should start culling.
185 // We need to clear out the highest frequencies to band-limit the waveform.
186 unsigned numberOfPartials = numberOfPartialsForRange(rangeIndex);
188 // Cull the aliasing partials for this pitch range.
189 for (i = numberOfPartials + 1; i < halfSize; ++i) {
193 // Clear packed-nyquist if necessary.
194 if (numberOfPartials < halfSize)
197 // Clear any DC-offset.
200 // Create the band-limited table.
201 OwnPtr<AudioFloatArray> table = adoptPtr(new AudioFloatArray(m_periodicWaveSize));
202 m_bandLimitedTables.append(table.release());
204 // Apply an inverse FFT to generate the time-domain table data.
205 float* data = m_bandLimitedTables[rangeIndex]->data();
206 frame.doInverseFFT(data);
208 // For the first range (which has the highest power), calculate its peak value then compute normalization scale.
211 vmaxmgv(data, 1, &maxValue, m_periodicWaveSize);
214 normalizationScale = 1.0f / maxValue;
217 // Apply normalization scale.
218 vsmul(data, 1, &normalizationScale, data, 1, m_periodicWaveSize);
222 void PeriodicWave::generateBasicWaveform(int shape)
224 unsigned fftSize = periodicWaveSize();
225 unsigned halfSize = fftSize / 2;
227 AudioFloatArray real(halfSize);
228 AudioFloatArray imag(halfSize);
229 float* realP = real.data();
230 float* imagP = imag.data();
232 // Clear DC and Nyquist.
236 for (unsigned n = 1; n < halfSize; ++n) {
237 float piFactor = 2 / (n * piFloat);
239 // All waveforms are odd functions with a positive slope at time 0. Hence the coefficients
240 // for cos() are always 0.
242 // Fourier coefficients according to standard definition:
243 // b = 1/pi*integrate(f(x)*sin(n*x), x, -pi, pi)
244 // = 2/pi*integrate(f(x)*sin(n*x), x, 0, pi)
245 // since f(x) is an odd function.
247 float b; // Coefficient for sin().
249 // Calculate Fourier coefficients depending on the shape. Note that the overall scaling
250 // (magnitude) of the waveforms is normalized in createBandLimitedTables().
252 case OscillatorNode::SINE:
253 // Standard sine wave function.
254 b = (n == 1) ? 1 : 0;
256 case OscillatorNode::SQUARE:
257 // Square-shaped waveform with the first half its maximum value and the second half its
260 // See http://mathworld.wolfram.com/FourierSeriesSquareWave.html
262 // b[n] = 2/n/pi*(1-(-1)^n)
263 // = 4/n/pi for n odd and 0 otherwise.
264 // = 2*(2/(n*pi)) for n odd
265 b = (n & 1) ? 2 * piFactor : 0;
267 case OscillatorNode::SAWTOOTH:
268 // Sawtooth-shaped waveform with the first half ramping from zero to maximum and the
269 // second half from minimum to zero.
271 // b[n] = -2*(-1)^n/pi/n
272 // = (2/(n*pi))*(-1)^(n+1)
273 b = piFactor * ((n & 1) ? 1 : -1);
275 case OscillatorNode::TRIANGLE:
276 // Triangle-shaped waveform going from 0 at time 0 to 1 at time pi/2 and back to 0 at
279 // See http://mathworld.wolfram.com/FourierSeriesTriangleWave.html
281 // b[n] = 8*sin(pi*k/2)/(pi*k)^2
282 // = 8/pi^2/n^2*(-1)^((n-1)/2) for n odd and 0 otherwise
283 // = 2*(2/(n*pi))^2 * (-1)^((n-1)/2)
285 b = 2 * (piFactor * piFactor) * ((((n - 1) >> 1) & 1) ? -1 : 1);
291 ASSERT_NOT_REACHED();
300 createBandLimitedTables(realP, imagP, halfSize);
303 } // namespace WebCore
305 #endif // ENABLE(WEB_AUDIO)