--- /dev/null
+#include <stdio.h>
+#include <stdlib.h>
+#include <unistd.h>
+#include <fcntl.h>
+#include <complex>
+#include <cassert>
+#include <algorithm>
+#include <fftw3.h>
+#include "pitchdetector.h"
+
+PitchDetector::PitchDetector(unsigned sample_rate, unsigned fft_length, unsigned pad_factor, unsigned overlap)
+ : sample_rate(sample_rate), fft_length(fft_length), pad_factor(pad_factor), overlap(overlap)
+{
+ in = reinterpret_cast<double *> (fftw_malloc(sizeof(double) * fft_length / pad_factor));
+ in_windowed = reinterpret_cast<double *> (fftw_malloc(sizeof(double) * fft_length));
+ out = reinterpret_cast<std::complex<double> *> (fftw_malloc(sizeof(std::complex<double>) * (fft_length / 2 + 1)));
+ bins = reinterpret_cast<double *> (fftw_malloc(sizeof(double) * (fft_length / 2 + 1)));
+
+ memset(in, 0, sizeof(double) * fft_length / pad_factor);
+
+ plan = fftw_plan_dft_r2c_1d(fft_length, in_windowed, reinterpret_cast<fftw_complex *> (out), FFTW_ESTIMATE);
+
+ // Initialize the Hamming window
+ window_data = new double[fft_length / pad_factor];
+ for (unsigned i = 0; i < fft_length / pad_factor; ++i) {
+ window_data[i] = 0.54 - 0.46 * cos(2.0 * M_PI * double(i) / double(fft_length/pad_factor - 1));
+ }
+}
+
+PitchDetector::~PitchDetector()
+{
+ fftw_free(in);
+ fftw_free(in_windowed);
+ fftw_free(out);
+ fftw_free(bins);
+}
+
+std::pair<double, double> PitchDetector::detect_pitch(short *buf)
+{
+ unsigned buf_len = fft_length / pad_factor / overlap;
+ memmove(in, in + buf_len, (fft_length - buf_len) * sizeof(double));
+
+ for (unsigned i = 0; i < buf_len; ++i)
+ in[i + (fft_length / pad_factor - buf_len)] = double(buf[i]);
+
+ apply_window(in, in_windowed, fft_length);
+ fftw_execute(plan);
+ find_peak_magnitudes(out, bins, fft_length);
+ std::pair<double, double> peak = find_peak(bins, fft_length);
+ if (peak.first > 0.0)
+ peak = adjust_for_overtones(peak, bins, fft_length);
+
+ return peak;
+}
+
+// Apply a standard Hamming window to our input data.
+void PitchDetector::apply_window(double *in, double *out, unsigned num_samples)
+{
+ for (unsigned i = 0; i < num_samples / pad_factor; ++i) {
+ out[i] = in[i] * window_data[i];
+ }
+ for (unsigned i = num_samples / pad_factor; i < num_samples; ++i) {
+ out[i] = 0.0;
+ }
+}
+
+void PitchDetector::find_peak_magnitudes(std::complex<double> *in, double *out, unsigned num_samples)
+{
+ for (unsigned i = 0; i < num_samples / 2 + 1; ++i)
+ out[i] = abs(in[i]);
+}
+
+std::pair<double, double> PitchDetector::find_peak(double *in, unsigned num_samples)
+{
+ double best_peak = in[5];
+ unsigned best_bin = 5;
+
+ for (unsigned i = 6; i < num_samples / 2 + 1; ++i) {
+ if (in[i] > best_peak) {
+ best_peak = in[i];
+ best_bin = i;
+ }
+ }
+
+ if (best_bin == 0 || best_bin == num_samples / 2) {
+ return std::make_pair(-1.0, 0.0);
+ }
+
+#if 0
+ printf("undertone strength: %+4.2f %+4.2f %+4.2f [%+4.2f] %+4.2f %+4.2f %+4.2f\n",
+ 20.0 * log10(in[best_bin*4] / fft_length),
+ 20.0 * log10(in[best_bin*3] / fft_length),
+ 20.0 * log10(in[best_bin*2] / fft_length),
+ 20.0 * log10(in[best_bin] / fft_length),
+ 20.0 * log10(in[best_bin/2] / fft_length),
+ 20.0 * log10(in[best_bin/3] / fft_length),
+ 20.0 * log10(in[best_bin/4] / fft_length));
+#endif
+
+ // see if we might have hit an overtone (set a limit of 5dB)
+ for (unsigned i = 4; i >= 1; --i) {
+ if (best_bin != best_bin / i &&
+ 20.0 * log10(in[best_bin] / in[best_bin / i]) < 5.0f) {
+#if 0
+ printf("Overtone of degree %u!\n", i);
+#endif
+ best_bin /= i;
+
+ // consider sliding one bin up or down
+ if (best_bin > 1 && in[best_bin - 1] > in[best_bin] && in[best_bin - 1] > in[best_bin - 2]) {
+ --best_bin;
+ } else if (best_bin < num_samples / 2 - 1 && in[best_bin + 1] > in[best_bin] && in[best_bin + 1] > in[best_bin + 2]) {
+ ++best_bin;
+ }
+
+ break;
+ }
+ }
+
+ if (best_bin == 0 || best_bin == num_samples / 2) {
+ return std::make_pair(-1.0, 0.0);
+ }
+ std::pair<double, double> peak =
+ interpolate_peak(in[best_bin - 1],
+ in[best_bin],
+ in[best_bin + 1]);
+
+ return std::make_pair(bin_to_freq(double(best_bin) + peak.first, num_samples), peak.second);
+}
+
+// it's perhaps not ideal to _first_ find the peak and _then_ the harmonics --
+// ideally, one should find the set of all peaks and then determine the likely
+// base from that... something for later. :-)
+std::pair<double, double> PitchDetector::adjust_for_overtones(std::pair<double, double> base, double *in, unsigned num_samples)
+{
+ double mu = base.first, var = 1.0 / (base.second * base.second);
+
+ //printf("Base at %.2f (amp=%5.2fdB)\n", base.first, base.second);
+
+ for (unsigned i = 2; i < 10; ++i) {
+ unsigned middle = unsigned(floor(freq_to_bin(base.first, num_samples) * i + 0.5));
+ unsigned lower = middle - (i+1)/2, upper = middle + (i+1)/2;
+
+ if (lower < 1)
+ lower = 1;
+ if (upper >= num_samples)
+ upper = num_samples - 2;
+
+ // printf("Searching in [%u,%u] = %f..%f\n", lower, upper, bin_to_freq(lower, num_samples), bin_to_freq(upper, num_samples));
+
+ // search for a peak in this interval
+ double best_harmonics_freq = -1.0;
+ double best_harmonics_amp = -1.0;
+ for (unsigned j = lower; j <= upper; ++j) {
+ if (in[j] > in[j-1] && in[j] > in[j+1]) {
+ std::pair<double, double> peak =
+ interpolate_peak(in[j - 1],
+ in[j],
+ in[j + 1]);
+
+ if (peak.second > best_harmonics_amp) {
+ best_harmonics_freq = bin_to_freq(j + peak.first, num_samples);
+ best_harmonics_amp = peak.second;
+ }
+ }
+ }
+
+ if (best_harmonics_amp <= 0.0)
+ continue;
+
+ //printf("Found overtone %u at %.2f (amp=%5.2fdB)\n", i, best_harmonics_freq,
+ // best_harmonics_amp);
+
+ double this_mu = best_harmonics_freq / double(i);
+ double this_var = 1.0 / (best_harmonics_amp * best_harmonics_amp);
+
+ double k = var / (var + this_var);
+ mu = (1.0 - k) * mu + k * this_mu;
+ var *= (1.0 - k);
+ }
+ return std::make_pair(mu, base.second);
+}
+
+double PitchDetector::bin_to_freq(double bin, unsigned num_samples)
+{
+ return bin * sample_rate / double(num_samples);
+}
+double PitchDetector::freq_to_bin(double freq, unsigned num_samples)
+{
+ return freq * double(num_samples) / double(sample_rate);
+}
+
+/*
+ * Given three bins, find the interpolated real peak based
+ * on their magnitudes. To do this, we execute the following
+ * plan:
+ *
+ * Fit a polynomial of the form ax^2 + bx + c = 0 to the data
+ * we have. Maple readily yields our coefficients, assuming
+ * that we have the values at x=-1, x=0 and x=1:
+ *
+ * > f := x -> a*x^2 + b*x + c;
+ *
+ * 2
+ * f := x -> a x + b x + c
+ *
+ * > cf := solve({ f(-1) = ym1, f(0) = y0, f(1) = y1 }, { a, b, c });
+ *
+ * y1 ym1 y1 ym1
+ * cf := {c = y0, b = ---- - ---, a = ---- + --- - y0}
+ * 2 2 2 2
+ *
+ * Now let's find the maximum point for the polynomial (it has to be
+ * a maximum, since y0 is the greatest value):
+ *
+ * > xmax := solve(subs(cf, diff(f(x), x)) = 0, x);
+ *
+ * -y1 + ym1
+ * xmax := -------------------
+ * 2 (y1 + ym1 - 2 y0)
+ *
+ * We could go further and insert {fmax,a,b,c} into the original
+ * polynomial, but it just gets hairy. We calculate a, b and c separately
+ * instead.
+ *
+ * http://www-ccrma.stanford.edu/~jos/parshl/Peak_Detection_Steps_3.html
+ * claims that detection is almost twice as good when using dB scale instead
+ * of linear scale for the input values, so we use that. (As a tiny bonus,
+ * we get back dB scale from the function.)
+ */
+std::pair<double, double> PitchDetector::interpolate_peak(double ym1, double y0, double y1)
+{
+ ym1 = log10(ym1);
+ y0 = log10(y0);
+ y1 = log10(y1);
+
+#if 0
+ assert(y0 >= y1);
+ assert(y0 >= ym1);
+#endif
+
+ double a = 0.5 * y1 + 0.5 * ym1 - y0;
+ double b = 0.5 * y1 - 0.5 * ym1;
+ double c = y0;
+
+ double xmax = (ym1 - y1) / (2.0 * (y1 + ym1 - 2.0 * y0));
+ double ymax = 20.0 * (a * xmax * xmax + b * xmax + c) - 90.0;
+
+ return std::make_pair(xmax, ymax);
+}
+
projects / pitch / blobdiff