git.sesse.net Git - pitch/blob - pitchdetector.cpp

   1 #include <stdio.h>
   2 #include <stdlib.h>
   3 #include <unistd.h>
   4 #include <fcntl.h>
   5 #include <complex>
   6 #include <cassert>
   7 #include <algorithm>
   8 #include <fftw3.h>
   9 #include "pitchdetector.h"
  10
  11 PitchDetector::PitchDetector(unsigned sample_rate, unsigned fft_length, unsigned pad_factor, unsigned overlap)
  12         : sample_rate(sample_rate), fft_length(fft_length), pad_factor(pad_factor), overlap(overlap)
  13 {
  14         in = reinterpret_cast<double *> (fftw_malloc(sizeof(double) * fft_length / pad_factor));
  15         in_windowed = reinterpret_cast<double *> (fftw_malloc(sizeof(double) * fft_length));
  16         out = reinterpret_cast<std::complex<double> *> (fftw_malloc(sizeof(std::complex<double>) * (fft_length / 2 + 1)));
  17         bins = reinterpret_cast<double *> (fftw_malloc(sizeof(double) * (fft_length / 2 + 1)));
  18
  19         memset(in, 0, sizeof(double) * fft_length / pad_factor);
  20
  21         plan = fftw_plan_dft_r2c_1d(fft_length, in_windowed, reinterpret_cast<fftw_complex *> (out), FFTW_ESTIMATE);
  22
  23         // Initialize the Hamming window
  24         window_data = new double[fft_length / pad_factor];
  25         for (unsigned i = 0; i < fft_length / pad_factor; ++i) {
  26                 window_data[i] = 0.54 - 0.46 * cos(2.0 * M_PI * double(i) / double(fft_length/pad_factor - 1));
  27         }
  28 }
  29
  30 PitchDetector::~PitchDetector()
  31 {
  32         fftw_free(in);
  33         fftw_free(in_windowed);
  34         fftw_free(out);
  35         fftw_free(bins);
  36 }
  37
  38 std::pair<double, double> PitchDetector::detect_pitch(short *buf)
  39 {
  40         unsigned buf_len = fft_length / pad_factor / overlap;
  41         memmove(in, in + buf_len, (fft_length - buf_len) * sizeof(double));
  42
  43         for (unsigned i = 0; i < buf_len; ++i)
  44                 in[i + (fft_length / pad_factor - buf_len)] = double(buf[i]);
  45
  46         apply_window(in, in_windowed, fft_length);
  47         fftw_execute(plan);
  48         find_peak_magnitudes(out, bins, fft_length);
  49         std::pair<double, double> peak = find_peak(bins, fft_length);
  50         if (peak.first > 0.0)
  51                 peak = adjust_for_overtones(peak, bins, fft_length);
  52
  53         return peak;
  54 }
  55
  56 // Apply a standard Hamming window to our input data.
  57 void PitchDetector::apply_window(double *in, double *out, unsigned num_samples)
  58 {
  59         for (unsigned i = 0; i < num_samples / pad_factor; ++i) {
  60                 out[i] = in[i] * window_data[i];
  61         }
  62         for (unsigned i = num_samples / pad_factor; i < num_samples; ++i) {
  63                 out[i] = 0.0;
  64         }
  65 }
  66
  67 void PitchDetector::find_peak_magnitudes(std::complex<double> *in, double *out, unsigned num_samples)
  68 {
  69         for (unsigned i = 0; i < num_samples / 2 + 1; ++i)
  70                 out[i] = abs(in[i]);
  71 }
  72
  73 std::pair<double, double> PitchDetector::find_peak(double *in, unsigned num_samples)
  74 {
  75         double best_peak = in[5];
  76         unsigned best_bin = 5;
  77
  78         for (unsigned i = 6; i < num_samples / 2 + 1; ++i) {
  79                 if (in[i] > best_peak) {
  80                         best_peak = in[i];
  81                         best_bin = i;
  82                 }
  83         }
  84
  85         if (best_bin == 0 || best_bin == num_samples / 2) {
  86                 return std::make_pair(-1.0, 0.0);
  87         }
  88
  89 #if 0
  90         printf("undertone strength: %+4.2f %+4.2f %+4.2f [%+4.2f] %+4.2f %+4.2f %+4.2f\n",
  91                 20.0 * log10(in[best_bin*4] / fft_length),
  92                 20.0 * log10(in[best_bin*3] / fft_length),
  93                 20.0 * log10(in[best_bin*2] / fft_length),
  94                 20.0 * log10(in[best_bin] / fft_length),
  95                 20.0 * log10(in[best_bin/2] / fft_length),
  96                 20.0 * log10(in[best_bin/3] / fft_length),
  97                 20.0 * log10(in[best_bin/4] / fft_length));
  98 #endif
  99
 100         // see if we might have hit an overtone (set a limit of 5dB)
 101         for (unsigned i = 4; i >= 1; --i) {
 102                 if (best_bin != best_bin / i &&
 103                     20.0 * log10(in[best_bin] / in[best_bin / i]) < 5.0f) {
 104 #if 0
 105                         printf("Overtone of degree %u!\n", i);
 106 #endif
 107                         best_bin /= i;
 108
 109                         // consider sliding one bin up or down
 110                         if (best_bin > 1 && in[best_bin - 1] > in[best_bin] && in[best_bin - 1] > in[best_bin - 2]) {
 111                                 --best_bin;
 112                         } else if (best_bin < num_samples / 2 - 1 && in[best_bin + 1] > in[best_bin] && in[best_bin + 1] > in[best_bin + 2]) {
 113                                 ++best_bin;
 114                         }
 115
 116                         break;
 117                 }
 118         }
 119
 120         if (best_bin == 0 || best_bin == num_samples / 2) {
 121                 return std::make_pair(-1.0, 0.0);
 122         }
 123         std::pair<double, double> peak =
 124                 interpolate_peak(in[best_bin - 1],
 125                                  in[best_bin],
 126                                  in[best_bin + 1]);
 127
 128         return std::make_pair(bin_to_freq(double(best_bin) + peak.first, num_samples), peak.second);
 129 }
 130
 131 // it's perhaps not ideal to _first_ find the peak and _then_ the harmonics --
 132 // ideally, one should find the set of all peaks and then determine the likely
 133 // base from that... something for later. :-)
 134 std::pair<double, double> PitchDetector::adjust_for_overtones(std::pair<double, double> base, double *in, unsigned num_samples)
 135 {
 136         double mu = base.first, var = 1.0 / (base.second * base.second);
 137
 138         //printf("Base at %.2f (amp=%5.2fdB)\n", base.first, base.second);
 139
 140         for (unsigned i = 2; i < 10; ++i) {
 141                 unsigned middle = unsigned(floor(freq_to_bin(base.first, num_samples) * i + 0.5));
 142                 unsigned lower = middle - (i+1)/2, upper = middle + (i+1)/2;
 143
 144                 if (lower < 1)
 145                         lower = 1;
 146                 if (upper >= num_samples)
 147                         upper = num_samples - 2;
 148
 149                 // printf("Searching in [%u,%u] = %f..%f\n", lower, upper, bin_to_freq(lower, num_samples), bin_to_freq(upper, num_samples));
 150
 151                 // search for a peak in this interval
 152                 double best_harmonics_freq = -1.0;
 153                 double best_harmonics_amp = -1.0;
 154                 for (unsigned j = lower; j <= upper; ++j) {
 155                         if (in[j] > in[j-1] && in[j] > in[j+1]) {
 156                                 std::pair<double, double> peak =
 157                                         interpolate_peak(in[j - 1],
 158                                                 in[j],
 159                                                 in[j + 1]);
 160
 161                                 if (peak.second > best_harmonics_amp) {
 162                                         best_harmonics_freq = bin_to_freq(j + peak.first, num_samples);
 163                                         best_harmonics_amp = peak.second;
 164                                 }
 165                         }
 166                 }
 167
 168                 if (best_harmonics_amp <= 0.0)
 169                         continue;
 170
 171                 //printf("Found overtone %u at %.2f (amp=%5.2fdB)\n", i, best_harmonics_freq,
 172                 //       best_harmonics_amp);
 173
 174                 double this_mu = best_harmonics_freq / double(i);
 175                 double this_var = 1.0 / (best_harmonics_amp * best_harmonics_amp);
 176
 177                 double k = var / (var + this_var);
 178                 mu = (1.0 - k) * mu + k * this_mu;
 179                 var *= (1.0 - k);
 180         }
 181         return std::make_pair(mu, base.second);
 182 }
 183
 184 double PitchDetector::bin_to_freq(double bin, unsigned num_samples)
 185 {
 186         return bin * sample_rate / double(num_samples);
 187 }
 188 double PitchDetector::freq_to_bin(double freq, unsigned num_samples)
 189 {
 190         return freq * double(num_samples) / double(sample_rate);
 191 }
 192
 193 /*
 194  * Given three bins, find the interpolated real peak based
 195  * on their magnitudes. To do this, we execute the following
 196  * plan:
 197  *
 198  * Fit a polynomial of the form ax^2 + bx + c = 0 to the data
 199  * we have. Maple readily yields our coefficients, assuming
 200  * that we have the values at x=-1, x=0 and x=1:
 201  *
 202  * > f := x -> a*x^2 + b*x + c;
 203  *
 204  *                               2
 205  *           f := x -> a x  + b x + c
 206  *
 207  * > cf := solve({ f(-1) = ym1, f(0) = y0, f(1) = y1 }, { a, b, c });
 208  *
 209  *                            y1    ym1       y1    ym1
 210  *        cf := {c = y0, b = ---- - ---, a = ---- + --- - y0}
 211  *                            2      2        2      2
 212  *
 213  * Now let's find the maximum point for the polynomial (it has to be
 214  * a maximum, since y0 is the greatest value):
 215  *
 216  * > xmax := solve(subs(cf, diff(f(x), x)) = 0, x);
 217  *
 218  *                                -y1 + ym1
 219  *                   xmax := -------------------
 220  *                           2 (y1 + ym1 - 2 y0)
 221  *
 222  * We could go further and insert {fmax,a,b,c} into the original
 223  * polynomial, but it just gets hairy. We calculate a, b and c separately
 224  * instead.
 225  *
 226  * http://www-ccrma.stanford.edu/~jos/parshl/Peak_Detection_Steps_3.html
 227  * claims that detection is almost twice as good when using dB scale instead
 228  * of linear scale for the input values, so we use that. (As a tiny bonus,
 229  * we get back dB scale from the function.)
 230  */
 231 std::pair<double, double> PitchDetector::interpolate_peak(double ym1, double y0, double y1)
 232 {
 233         ym1 = log10(ym1);
 234         y0 = log10(y0);
 235         y1 = log10(y1);
 236
 237 #if 0
 238         assert(y0 >= y1);
 239         assert(y0 >= ym1);
 240 #endif
 241
 242         double a = 0.5 * y1 + 0.5 * ym1 - y0;
 243         double b = 0.5 * y1 - 0.5 * ym1;
 244         double c = y0;
 245
 246         double xmax = (ym1 - y1) / (2.0 * (y1 + ym1 - 2.0 * y0));
 247         double ymax = 20.0 * (a * xmax * xmax + b * xmax + c) - 90.0;
 248
 249         return std::make_pair(xmax, ymax);
 250 }
 251