static autoSpectrum Cepstrum_to_Spectrum2 (Cepstrum me) { //TODO power cepstrum
try {
autoNUMfft_Table fftTable;
long numberOfSamples = 2 * my nx - 2;
autoNUMvector<double> fftbuf (1, numberOfSamples);
autoSpectrum thee = Spectrum_create (0.5 / my dx, my nx);
fftbuf[1] = sqrt (my z[1][1]);
for (long i = 2; i <= my nx; i++) {
fftbuf[i] = 2.0 * sqrt (my z[1][i]);
}
// fftbuf[my nx+1 ... numberOfSamples] = 0
NUMfft_Table_init (&fftTable, numberOfSamples);
NUMfft_forward (&fftTable, fftbuf.peek());
thy z[1][1] = fabs (fftbuf[1]);
for (long i = 2; i < my nx; i++) {
double br = fftbuf[i + i - 2], bi = fftbuf[i + i - 1];
thy z[1][i] = sqrt (br * br + bi * bi);
}
thy z[1][my nx] = fabs (fftbuf[numberOfSamples]);
for (long i = 1; i <= my nx; i++) {
thy z[1][i] = exp (NUMln10 * thy z[1][i] / 20.0) * 2e-5 / sqrt (2 * thy dx);
thy z[2][i] = 0.0;
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": no Spectrum created.");
}
}
static autoCepstrum Spectrum_to_Cepstrum2 (Spectrum me) {
try {
autoNUMfft_Table fftTable;
// originalNumberOfSamplesProbablyOdd irrelevant
if (my x1 != 0.0) {
Melder_throw (U"A Fourier-transformable Spectrum must have a first frequency of 0 Hz, not ", my x1, U" Hz.");
}
long numberOfSamples = 2 * my nx - 2;
autoCepstrum thee = Cepstrum_create (0.5 / my dx, my nx);
// my dx = 1 / (dT * N) = 1 / (duration of sound)
thy dx = 1 / (my dx * numberOfSamples); // Cepstrum is on [-T/2, T/2] !
NUMfft_Table_init (&fftTable, numberOfSamples);
autoNUMvector<double> fftbuf (1, numberOfSamples);
fftbuf[1] = my v_getValueAtSample (1, 0, 2);
for (long i = 2; i < my nx; i++) {
fftbuf [i + i - 2] = my v_getValueAtSample (i, 0, 2);
fftbuf [i + i - 1] = 0.0;
}
fftbuf [numberOfSamples] = my v_getValueAtSample (my nx, 0, 2);
NUMfft_backward (&fftTable, fftbuf.peek());
for (long i = 1; i <= my nx; i++) {
double val = fftbuf[i] / numberOfSamples; // scaling 1/n because ifft(fft(1))= n;
thy z[1][i] = val * val; // power cepstrum
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": not converted to Cepstrum.");
}
}
PowerCepstrogram Sound_to_PowerCepstrogram_hillenbrand (Sound me, double minimumPitch, double dt) {
try {
// minimum analysis window has 3 periods of lowest pitch
double analysisWidth = 3 / minimumPitch;
if (analysisWidth > my dx * my nx) {
analysisWidth = my dx * my nx;
}
double t1, samplingFrequency = 1 / my dx;
autoSound thee;
if (samplingFrequency > 30000) {
samplingFrequency = samplingFrequency / 2;
thee.reset (Sound_resample (me, samplingFrequency, 1));
} else {
thee.reset (Data_copy (me));
}
// pre-emphasis with fixed coefficient 0.9
for (long i = thy nx; i > 1; i--) {
thy z[1][i] -= 0.9 * thy z[1][i - 1];
}
long nosInWindow = analysisWidth * samplingFrequency, nFrames;
if (nosInWindow < 8) {
Melder_throw ("Analysis window too short.");
}
Sampled_shortTermAnalysis (thee.peek(), analysisWidth, dt, & nFrames, & t1);
autoNUMvector<double> hamming (1, nosInWindow);
for (long i = 1; i <= nosInWindow; i++) {
hamming[i] = 0.54 -0.46 * cos(2 * NUMpi * (i - 1) / (nosInWindow - 1));
}
long nfft = 8; // minimum possible
while (nfft < nosInWindow) { nfft *= 2; }
long nfftdiv2 = nfft / 2;
autoNUMvector<double> fftbuf (1, nfft); // "complex" array
autoNUMvector<double> spectrum (1, nfftdiv2 + 1); // +1 needed
autoNUMfft_Table fftTable;
NUMfft_Table_init (&fftTable, nfft); // sound to spectrum
double qmax = 0.5 * nfft / samplingFrequency, dq = qmax / (nfftdiv2 + 1);
autoPowerCepstrogram him = PowerCepstrogram_create (my xmin, my xmax, nFrames, dt, t1, 0, qmax, nfftdiv2+1, dq, 0);
autoMelderProgress progress (L"Cepstrogram analysis");
for (long iframe = 1; iframe <= nFrames; iframe++) {
double tbegin = t1 + (iframe - 1) * dt - analysisWidth / 2;
tbegin = tbegin < thy xmin ? thy xmin : tbegin;
long istart = Sampled_xToIndex (thee.peek(), tbegin);
istart = istart < 1 ? 1 : istart;
long iend = istart + nosInWindow - 1;
iend = iend > thy nx ? thy nx : iend;
for (long i = 1; i <= nosInWindow; i++) {
fftbuf[i] = thy z[1][istart + i - 1] * hamming[i];
}
for (long i = nosInWindow + 1; i <= nfft; i++) {
fftbuf[i] = 0;
}
NUMfft_forward (&fftTable, fftbuf.peek());
complexfftoutput_to_power (fftbuf.peek(), nfft, spectrum.peek(), true); // log10(|fft|^2)
// subtract average
double specmean = spectrum[1];
for (long i = 2; i <= nfftdiv2 + 1; i++) {
specmean += spectrum[i];
}
specmean /= nfftdiv2 + 1;
for (long i = 1; i <= nfftdiv2 + 1; i++) {
spectrum[i] -= specmean;
}
/*
* Here we diverge from Hillenbrand as he takes the fft of half of the spectral values.
* H. forgets that the actual spectrum has nfft/2+1 values. Thefore, we take the inverse
* transform because this keeps the number of samples a power of 2.
* At the same time this results in twice as much numbers in the quefrency domain, i.e. we end with nfft/2+1
* numbers while H. has only nfft/4!
*/
fftbuf[1] = spectrum[1];
for (long i = 2; i < nfftdiv2 + 1; i++) {
fftbuf[i+i-2] = spectrum[i];
fftbuf[i+i-1] = 0;
}
fftbuf[nfft] = spectrum[nfftdiv2 + 1];
NUMfft_backward (&fftTable, fftbuf.peek());
for (long i = 1; i <= nfftdiv2 + 1; i++) {
his z[i][iframe] = fftbuf[i] * fftbuf[i];
}
if ((iframe % 10) == 1) {
Melder_progress ((double) iframe / nFrames, L"Cepstrogram analysis of frame ",
Melder_integer (iframe), L" out of ", Melder_integer (nFrames), L".");
}
}
return him.transfer();
} catch (MelderError) {
Melder_throw (me, ": no Cepstrogram created.");
}
}
