9 #include "pitchdetector.h"
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)
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)));
19 memset(in, 0, sizeof(double) * fft_length / pad_factor);
21 plan = fftw_plan_dft_r2c_1d(fft_length, in_windowed, reinterpret_cast<fftw_complex *> (out), FFTW_ESTIMATE);
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));
30 PitchDetector::~PitchDetector()
33 fftw_free(in_windowed);
38 std::pair<double, double> PitchDetector::detect_pitch(short *buf)
40 unsigned buf_len = fft_length / pad_factor / overlap;
41 memmove(in, in + buf_len, (fft_length / pad_factor - buf_len) * sizeof(double));
43 for (unsigned i = 0; i < buf_len; ++i)
44 in[i + (fft_length / pad_factor - buf_len)] = double(buf[i]);
46 apply_window(in, in_windowed, fft_length);
48 find_peak_magnitudes(out, bins, fft_length);
49 std::pair<double, double> peak = find_peak(bins, fft_length);
51 peak = adjust_for_overtones(peak, bins, fft_length);
56 // Apply a standard Hamming window to our input data.
57 void PitchDetector::apply_window(double *in, double *out, unsigned num_samples)
59 for (unsigned i = 0; i < num_samples / pad_factor; ++i) {
60 out[i] = in[i] * window_data[i];
62 for (unsigned i = num_samples / pad_factor; i < num_samples; ++i) {
67 void PitchDetector::find_peak_magnitudes(std::complex<double> *in, double *out, unsigned num_samples)
69 for (unsigned i = 0; i < num_samples / 2 + 1; ++i)
73 std::pair<double, double> PitchDetector::find_peak(double *in, unsigned num_samples)
75 double best_peak = in[5];
76 unsigned best_bin = 5;
78 for (unsigned i = 6; i < num_samples / 2 + 1; ++i) {
79 if (in[i] > best_peak) {
84 if (20.0 * log10(in[i] / fft_length) > 0.0) {
85 printf("PEAK: %+4.2f dB %5.2f Hz\n",
86 20.0 * log10(in[i] / fft_length),
87 bin_to_freq(i, num_samples));
92 if (best_bin == 0 || best_bin == num_samples / 2) {
93 return std::make_pair(-1.0, 0.0);
97 printf("undertone strength: %+4.2f %+4.2f %+4.2f [%+4.2f] %+4.2f %+4.2f %+4.2f\n",
98 20.0 * log10(in[best_bin*4] / fft_length),
99 20.0 * log10(in[best_bin*3] / fft_length),
100 20.0 * log10(in[best_bin*2] / fft_length),
101 20.0 * log10(in[best_bin] / fft_length),
102 20.0 * log10(in[best_bin/2] / fft_length),
103 20.0 * log10(in[best_bin/3] / fft_length),
104 20.0 * log10(in[best_bin/4] / fft_length));
107 // see if we might have hit an overtone (set a limit of 10dB)
108 for (unsigned i = 6; i >= 1; --i) {
109 if (best_bin != best_bin / i &&
110 20.0 * log10(in[best_bin] / in[best_bin / i]) < 10.0f &&
113 printf("Overtone of degree %u!\n", i);
117 // consider sliding one bin up or down
118 if (best_bin > 1 && in[best_bin - 1] > in[best_bin] && in[best_bin - 1] > in[best_bin - 2]) {
120 } else if (best_bin < num_samples / 2 - 1 && in[best_bin + 1] > in[best_bin] && in[best_bin + 1] > in[best_bin + 2]) {
128 if (best_bin == 0 || best_bin == num_samples / 2) {
129 return std::make_pair(-1.0, 0.0);
131 std::pair<double, double> peak =
132 interpolate_peak(in[best_bin - 1],
136 return std::make_pair(bin_to_freq(double(best_bin) + peak.first, num_samples), peak.second);
139 // it's perhaps not ideal to _first_ find the peak and _then_ the harmonics --
140 // ideally, one should find the set of all peaks and then determine the likely
141 // base from that... something for later. :-)
142 std::pair<double, double> PitchDetector::adjust_for_overtones(std::pair<double, double> base, double *in, unsigned num_samples)
144 double mu = base.first, var = 1.0 / (base.second * base.second);
146 //printf("Base at %.2f (amp=%5.2fdB)\n", base.first, base.second);
148 for (unsigned i = 2; i < 10; ++i) {
149 unsigned middle = unsigned(floor(freq_to_bin(base.first, num_samples) * i + 0.5));
150 unsigned lower = middle - (i+1)/2, upper = middle + (i+1)/2;
154 if (upper >= num_samples)
155 upper = num_samples - 2;
157 // printf("Searching in [%u,%u] = %f..%f\n", lower, upper, bin_to_freq(lower, num_samples), bin_to_freq(upper, num_samples));
159 // search for a peak in this interval
160 double best_harmonics_freq = -1.0;
161 double best_harmonics_amp = -1.0;
162 for (unsigned j = lower; j <= upper; ++j) {
163 if (in[j] > in[j-1] && in[j] > in[j+1]) {
164 std::pair<double, double> peak =
165 interpolate_peak(in[j - 1],
169 if (peak.second > best_harmonics_amp) {
170 best_harmonics_freq = bin_to_freq(j + peak.first, num_samples);
171 best_harmonics_amp = peak.second;
176 if (best_harmonics_amp <= 0.0)
179 //printf("Found overtone %u at %.2f (amp=%5.2fdB)\n", i, best_harmonics_freq,
180 // best_harmonics_amp);
182 double this_mu = best_harmonics_freq / double(i);
183 double this_var = 1.0 / (best_harmonics_amp * best_harmonics_amp);
185 double k = var / (var + this_var);
186 mu = (1.0 - k) * mu + k * this_mu;
189 return std::make_pair(mu, base.second);
192 double PitchDetector::bin_to_freq(double bin, unsigned num_samples)
194 return bin * sample_rate / double(num_samples);
196 double PitchDetector::freq_to_bin(double freq, unsigned num_samples)
198 return freq * double(num_samples) / double(sample_rate);
202 * Given three bins, find the interpolated real peak based
203 * on their magnitudes. To do this, we execute the following
206 * Fit a polynomial of the form ax^2 + bx + c = 0 to the data
207 * we have. Maple readily yields our coefficients, assuming
208 * that we have the values at x=-1, x=0 and x=1:
210 * > f := x -> a*x^2 + b*x + c;
213 * f := x -> a x + b x + c
215 * > cf := solve({ f(-1) = ym1, f(0) = y0, f(1) = y1 }, { a, b, c });
218 * cf := {c = y0, b = ---- - ---, a = ---- + --- - y0}
221 * Now let's find the maximum point for the polynomial (it has to be
222 * a maximum, since y0 is the greatest value):
224 * > xmax := solve(subs(cf, diff(f(x), x)) = 0, x);
227 * xmax := -------------------
228 * 2 (y1 + ym1 - 2 y0)
230 * We could go further and insert {fmax,a,b,c} into the original
231 * polynomial, but it just gets hairy. We calculate a, b and c separately
234 * http://www-ccrma.stanford.edu/~jos/parshl/Peak_Detection_Steps_3.html
235 * claims that detection is almost twice as good when using dB scale instead
236 * of linear scale for the input values, so we use that. (As a tiny bonus,
237 * we get back dB scale from the function.)
239 std::pair<double, double> PitchDetector::interpolate_peak(double ym1, double y0, double y1)
250 double a = 0.5 * y1 + 0.5 * ym1 - y0;
251 double b = 0.5 * y1 - 0.5 * ym1;
254 double xmax = (ym1 - y1) / (2.0 * (y1 + ym1 - 2.0 * y0));
255 double ymax = 20.0 * (a * xmax * xmax + b * xmax + c) - 70.0;
257 return std::make_pair(xmax, ymax);