std::unique_ptr<FFTFrame> FFTFrame::createInterpolatedFrame(const FFTFrame& frame1, const FFTFrame& frame2, double x)
{
std::unique_ptr<FFTFrame> newFrame(new FFTFrame(frame1.fftSize()));
newFrame->interpolateFrequencyComponents(frame1, frame2, x);
// In the time-domain, the 2nd half of the response must be zero, to avoid circular convolution aliasing...
int fftSize = newFrame->fftSize();
AudioFloatArray buffer(fftSize);
newFrame->doInverseFFT(buffer.data());
buffer.zeroRange(fftSize / 2, fftSize);
// Put back into frequency domain.
newFrame->doFFT(buffer.data());
return newFrame;
}
void FFTFrame::interpolateFrequencyComponents(const FFTFrame& frame1, const FFTFrame& frame2, double interp)
{
// FIXME : with some work, this method could be optimized
float* realP = realData();
float* imagP = imagData();
const float* realP1 = frame1.realData();
const float* imagP1 = frame1.imagData();
const float* realP2 = frame2.realData();
const float* imagP2 = frame2.imagData();
m_FFTSize = frame1.fftSize();
m_log2FFTSize = frame1.log2FFTSize();
double s1base = (1.0 - interp);
double s2base = interp;
double phaseAccum = 0.0;
double lastPhase1 = 0.0;
double lastPhase2 = 0.0;
realP[0] = static_cast<float>(s1base * realP1[0] + s2base * realP2[0]);
imagP[0] = static_cast<float>(s1base * imagP1[0] + s2base * imagP2[0]);
int n = m_FFTSize / 2;
for (int i = 1; i < n; ++i) {
Complex c1(realP1[i], imagP1[i]);
Complex c2(realP2[i], imagP2[i]);
double mag1 = abs(c1);
double mag2 = abs(c2);
// Interpolate magnitudes in decibels
double mag1db = 20.0 * log10(mag1);
double mag2db = 20.0 * log10(mag2);
double s1 = s1base;
double s2 = s2base;
double magdbdiff = mag1db - mag2db;
// Empirical tweak to retain higher-frequency zeroes
double threshold = (i > 16) ? 5.0 : 2.0;
if (magdbdiff < -threshold && mag1db < 0.0)
{
s1 = pow(s1, 0.75);
s2 = 1.0 - s1;
} else if (magdbdiff > threshold && mag2db < 0.0)
{
s2 = pow(s2, 0.75);
s1 = 1.0 - s2;
}
// Average magnitude by decibels instead of linearly
double magdb = s1 * mag1db + s2 * mag2db;
double mag = pow(10.0, 0.05 * magdb);
// Now, deal with phase
double phase1 = arg(c1);
double phase2 = arg(c2);
double deltaPhase1 = phase1 - lastPhase1;
double deltaPhase2 = phase2 - lastPhase2;
lastPhase1 = phase1;
lastPhase2 = phase2;
// Unwrap phase deltas
if (deltaPhase1 > piDouble)
deltaPhase1 -= 2.0 * piDouble;
if (deltaPhase1 < -piDouble)
deltaPhase1 += 2.0 * piDouble;
if (deltaPhase2 > piDouble)
deltaPhase2 -= 2.0 * piDouble;
if (deltaPhase2 < -piDouble)
deltaPhase2 += 2.0 * piDouble;
// Blend group-delays
double deltaPhaseBlend;
if (deltaPhase1 - deltaPhase2 > piDouble)
deltaPhaseBlend = s1 * deltaPhase1 + s2 * (2.0 * piDouble + deltaPhase2);
else if (deltaPhase2 - deltaPhase1 > piDouble)
deltaPhaseBlend = s1 * (2.0 * piDouble + deltaPhase1) + s2 * deltaPhase2;
else
deltaPhaseBlend = s1 * deltaPhase1 + s2 * deltaPhase2;
phaseAccum += deltaPhaseBlend;
// Unwrap
if (phaseAccum > piDouble)
phaseAccum -= 2.0 * piDouble;
if (phaseAccum < -piDouble)
phaseAccum += 2.0 * piDouble;
Complex c = std::polar(mag, phaseAccum);
realP[i] = static_cast<float>(c.real());
imagP[i] = static_cast<float>(c.imag());
}
}