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1 /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
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2 /*
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3 Permission is hereby granted, free of charge, to any person
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4 obtaining a copy of this software and associated documentation
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5 files (the "Software"), to deal in the Software without
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6 restriction, including without limitation the rights to use, copy,
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7 modify, merge, publish, distribute, sublicense, and/or sell copies
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8 of the Software, and to permit persons to whom the Software is
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9 furnished to do so, subject to the following conditions:
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10
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11 The above copyright notice and this permission notice shall be
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12 included in all copies or substantial portions of the Software.
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13
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14 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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15 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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16 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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17 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR
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18 ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
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19 CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
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20 WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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21 */
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22
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23 #include "CepstrumPitchTracker.h"
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24
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25 #include <vector>
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26 #include <algorithm>
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27
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28 #include <cstdio>
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29 #include <cmath>
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30 #include <complex>
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31
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32 using std::string;
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33 using std::vector;
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34
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35 CepstrumPitchTracker::Hypothesis::Hypothesis()
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36 {
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37 m_state = New;
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38 m_age = 0;
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39 }
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40
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41 CepstrumPitchTracker::Hypothesis::~Hypothesis()
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42 {
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43 }
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44
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45 bool
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46 CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s)
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47 {
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48 if (m_pending.empty()) {
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49 return true;
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50 }
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51 Estimate last = m_pending[m_pending.size()-1];
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52 double r = s.freq / last.freq;
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53 int cents = lrint(1200.0 * (log(r) / log(2.0)));
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54 return (cents > -200 && cents < 200);
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55 }
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56
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57 bool
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58 CepstrumPitchTracker::Hypothesis::isSatisfied()
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59 {
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60 return (m_pending.size() > 2);
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61 }
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62
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63 void
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64 CepstrumPitchTracker::Hypothesis::advanceTime()
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65 {
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66 ++m_age;
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67 }
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68
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69 bool
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70 CepstrumPitchTracker::Hypothesis::test(Estimate s)
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71 {
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72 bool accept = false;
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73
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74 switch (m_state) {
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75
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76 case New:
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77 m_state = Provisional;
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78 accept = true;
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79 break;
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80
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81 case Provisional:
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82 if (m_age > 3) {
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83 m_state = Rejected;
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84 } else if (isWithinTolerance(s)) {
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85 accept = true;
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86 }
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87 break;
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88
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89 case Satisfied:
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90 if (m_age > 3) {
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91 m_state = Expired;
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92 } else if (isWithinTolerance(s)) {
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93 accept = true;
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94 }
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95 break;
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96
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97 case Rejected:
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98 break;
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99
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100 case Expired:
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101 break;
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102 }
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103
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104 if (accept) {
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105 m_pending.push_back(s);
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106 m_age = 0;
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107 if (m_state == Provisional && isSatisfied()) {
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108 m_state = Satisfied;
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109 }
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110 }
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111
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112 return accept;
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113 }
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114
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115 CepstrumPitchTracker::Hypothesis::State
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116 CepstrumPitchTracker::Hypothesis::getState()
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117 {
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118 return m_state;
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119 }
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120
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121 int
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122 CepstrumPitchTracker::Hypothesis::getPendingLength()
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123 {
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124 return m_pending.size();
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125 }
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126
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127 CepstrumPitchTracker::Hypothesis::Estimates
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128 CepstrumPitchTracker::Hypothesis::getAcceptedEstimates()
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129 {
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130 if (m_state == Satisfied || m_state == Expired) {
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131 return m_pending;
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132 } else {
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133 return Estimates();
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134 }
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135 }
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136
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137 void
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138 CepstrumPitchTracker::Hypothesis::addFeatures(FeatureList &fl)
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139 {
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140 for (int i = 0; i < m_pending.size(); ++i) {
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141 Feature f;
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142 f.hasTimestamp = true;
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143 f.timestamp = m_pending[i].time;
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144 f.values.push_back(m_pending[i].freq);
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145 fl.push_back(f);
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146 }
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147 }
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148
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149 CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :
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150 Plugin(inputSampleRate),
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151 m_channels(0),
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152 m_stepSize(256),
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153 m_blockSize(1024),
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154 m_fmin(50),
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155 m_fmax(1000),
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156 m_histlen(1),
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157 m_vflen(3),
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158 m_binFrom(0),
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159 m_binTo(0),
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160 m_bins(0),
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161 m_history(0),
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162 m_prevpeak(0),
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163 m_prevprop(0)
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164 {
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165 }
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166
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167 CepstrumPitchTracker::~CepstrumPitchTracker()
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168 {
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169 if (m_history) {
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170 for (int i = 0; i < m_histlen; ++i) {
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171 delete[] m_history[i];
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172 }
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173 delete[] m_history;
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174 }
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175 }
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176
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177 string
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178 CepstrumPitchTracker::getIdentifier() const
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179 {
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180 return "cepstrum-pitch";
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181 }
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182
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183 string
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184 CepstrumPitchTracker::getName() const
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185 {
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186 return "Cepstrum Pitch Tracker";
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187 }
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188
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189 string
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190 CepstrumPitchTracker::getDescription() const
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191 {
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192 return "Estimate f0 of monophonic material using a cepstrum method.";
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193 }
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194
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195 string
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196 CepstrumPitchTracker::getMaker() const
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197 {
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198 return "Chris Cannam";
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199 }
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200
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201 int
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202 CepstrumPitchTracker::getPluginVersion() const
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203 {
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204 // Increment this each time you release a version that behaves
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205 // differently from the previous one
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206 return 1;
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207 }
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208
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209 string
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210 CepstrumPitchTracker::getCopyright() const
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211 {
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212 return "Freely redistributable (BSD license)";
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213 }
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214
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215 CepstrumPitchTracker::InputDomain
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216 CepstrumPitchTracker::getInputDomain() const
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217 {
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218 return FrequencyDomain;
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219 }
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220
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221 size_t
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222 CepstrumPitchTracker::getPreferredBlockSize() const
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223 {
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224 return 1024;
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225 }
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226
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227 size_t
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228 CepstrumPitchTracker::getPreferredStepSize() const
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229 {
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230 return 256;
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231 }
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232
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233 size_t
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234 CepstrumPitchTracker::getMinChannelCount() const
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235 {
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236 return 1;
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237 }
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238
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239 size_t
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240 CepstrumPitchTracker::getMaxChannelCount() const
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241 {
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242 return 1;
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243 }
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244
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245 CepstrumPitchTracker::ParameterList
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246 CepstrumPitchTracker::getParameterDescriptors() const
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247 {
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248 ParameterList list;
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249 return list;
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250 }
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251
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252 float
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253 CepstrumPitchTracker::getParameter(string identifier) const
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254 {
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255 return 0.f;
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256 }
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257
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258 void
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259 CepstrumPitchTracker::setParameter(string identifier, float value)
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260 {
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261 }
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262
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263 CepstrumPitchTracker::ProgramList
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264 CepstrumPitchTracker::getPrograms() const
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265 {
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266 ProgramList list;
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267 return list;
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268 }
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269
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270 string
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271 CepstrumPitchTracker::getCurrentProgram() const
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272 {
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273 return ""; // no programs
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274 }
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275
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276 void
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277 CepstrumPitchTracker::selectProgram(string name)
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278 {
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279 }
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280
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281 CepstrumPitchTracker::OutputList
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282 CepstrumPitchTracker::getOutputDescriptors() const
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283 {
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284 OutputList outputs;
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285
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286 int n = 0;
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287
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288 OutputDescriptor d;
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289
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290 d.identifier = "f0";
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291 d.name = "Estimated f0";
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292 d.description = "Estimated fundamental frequency";
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293 d.unit = "Hz";
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294 d.hasFixedBinCount = true;
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295 d.binCount = 1;
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296 d.hasKnownExtents = true;
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297 d.minValue = m_fmin;
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298 d.maxValue = m_fmax;
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299 d.isQuantized = false;
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300 d.sampleType = OutputDescriptor::FixedSampleRate;
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301 d.sampleRate = (m_inputSampleRate / m_stepSize);
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302 d.hasDuration = false;
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303 outputs.push_back(d);
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304
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305 return outputs;
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306 }
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307
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308 bool
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309 CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
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310 {
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311 if (channels < getMinChannelCount() ||
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312 channels > getMaxChannelCount()) return false;
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313
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314 // std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
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315 // << ", stepSize = " << stepSize << ", blockSize = " << blockSize
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316 // << std::endl;
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317
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318 m_channels = channels;
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319 m_stepSize = stepSize;
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320 m_blockSize = blockSize;
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321
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322 m_binFrom = int(m_inputSampleRate / m_fmax);
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323 m_binTo = int(m_inputSampleRate / m_fmin);
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324
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325 if (m_binTo >= (int)m_blockSize / 2) {
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326 m_binTo = m_blockSize / 2 - 1;
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327 }
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328
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329 m_bins = (m_binTo - m_binFrom) + 1;
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330
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331 m_history = new double *[m_histlen];
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332 for (int i = 0; i < m_histlen; ++i) {
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333 m_history[i] = new double[m_bins];
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334 }
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335
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336 reset();
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337
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338 return true;
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339 }
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340
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341 void
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342 CepstrumPitchTracker::reset()
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343 {
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344 for (int i = 0; i < m_histlen; ++i) {
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345 for (int j = 0; j < m_bins; ++j) {
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346 m_history[i][j] = 0.0;
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347 }
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348 }
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349 }
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350
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351 void
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352 CepstrumPitchTracker::filter(const double *cep, double *result)
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353 {
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354 int hix = m_histlen - 1; // current history index
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355
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356 // roll back the history
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357 if (m_histlen > 1) {
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358 double *oldest = m_history[0];
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359 for (int i = 1; i < m_histlen; ++i) {
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360 m_history[i-1] = m_history[i];
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361 }
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362 // and stick this back in the newest spot, to recycle
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363 m_history[hix] = oldest;
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364 }
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365
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366 for (int i = 0; i < m_bins; ++i) {
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367 double v = 0;
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368 int n = 0;
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369 // average according to the vertical filter length
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370 for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
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371 int ix = i + m_binFrom + j;
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372 if (ix >= 0 && ix < m_blockSize) {
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373 v += cep[ix];
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374 ++n;
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375 }
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376 }
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377 m_history[hix][i] = v / n;
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378 }
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379
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380 for (int i = 0; i < m_bins; ++i) {
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381 double mean = 0.0;
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382 for (int j = 0; j < m_histlen; ++j) {
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383 mean += m_history[j][i];
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384 }
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385 mean /= m_histlen;
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386 result[i] = mean;
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387 }
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388 }
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389
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390 double
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391 CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
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392 {
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393 double aroundPeak = data[n];
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394 double peakProportion = 0.0;
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395
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396 int i = n - 1;
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397 while (i > 0 && data[i] <= data[i+1]) {
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398 aroundPeak += fabs(data[i]);
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399 --i;
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400 }
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401 i = n + 1;
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402 while (i < m_bins && data[i] <= data[i-1]) {
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403 aroundPeak += fabs(data[i]);
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404 ++i;
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405 }
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406 peakProportion = aroundPeak / abstot;
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407
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408 return peakProportion;
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409 }
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410
|
Chris@11
|
411 bool
|
Chris@11
|
412 CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
|
Chris@11
|
413 {
|
Chris@11
|
414 bool accept = false;
|
Chris@11
|
415
|
Chris@11
|
416 if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
|
Chris@11
|
417 accept = true;
|
Chris@11
|
418 } else if (peakProportion > m_prevprop * 2) {
|
Chris@11
|
419 accept = true;
|
Chris@11
|
420 }
|
Chris@11
|
421
|
Chris@11
|
422 return accept;
|
Chris@11
|
423 }
|
Chris@11
|
424
|
Chris@8
|
425 CepstrumPitchTracker::FeatureSet
|
Chris@8
|
426 CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
|
Chris@8
|
427 {
|
Chris@8
|
428 FeatureSet fs;
|
Chris@8
|
429
|
Chris@8
|
430 int bs = m_blockSize;
|
Chris@8
|
431 int hs = m_blockSize/2 + 1;
|
Chris@8
|
432
|
Chris@8
|
433 double *rawcep = new double[bs];
|
Chris@8
|
434 double *io = new double[bs];
|
Chris@8
|
435 double *logmag = new double[bs];
|
Chris@8
|
436
|
Chris@9
|
437 // The "inverse symmetric" method. Seems to be the most reliable
|
Chris@8
|
438
|
Chris@8
|
439 for (int i = 0; i < hs; ++i) {
|
Chris@8
|
440
|
Chris@8
|
441 double power =
|
Chris@8
|
442 inputBuffers[0][i*2 ] * inputBuffers[0][i*2 ] +
|
Chris@8
|
443 inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
|
Chris@8
|
444 double mag = sqrt(power);
|
Chris@8
|
445
|
Chris@8
|
446 double lm = log(mag + 0.00000001);
|
Chris@8
|
447
|
Chris@9
|
448 logmag[i] = lm;
|
Chris@9
|
449 if (i > 0) logmag[bs - i] = lm;
|
Chris@8
|
450 }
|
Chris@8
|
451
|
Chris@9
|
452 fft(bs, true, logmag, 0, rawcep, io);
|
Chris@8
|
453
|
Chris@8
|
454 delete[] logmag;
|
Chris@8
|
455 delete[] io;
|
Chris@8
|
456
|
Chris@8
|
457 int n = m_bins;
|
Chris@8
|
458 double *data = new double[n];
|
Chris@8
|
459 filter(rawcep, data);
|
Chris@8
|
460 delete[] rawcep;
|
Chris@8
|
461
|
Chris@11
|
462 double abstot = 0.0;
|
Chris@11
|
463
|
Chris@11
|
464 for (int i = 0; i < n; ++i) {
|
Chris@11
|
465 abstot += fabs(data[i]);
|
Chris@11
|
466 }
|
Chris@11
|
467
|
Chris@8
|
468 double maxval = 0.0;
|
Chris@11
|
469 int maxbin = -1;
|
Chris@8
|
470
|
Chris@8
|
471 for (int i = 0; i < n; ++i) {
|
Chris@8
|
472 if (data[i] > maxval) {
|
Chris@8
|
473 maxval = data[i];
|
Chris@8
|
474 maxbin = i;
|
Chris@8
|
475 }
|
Chris@8
|
476 }
|
Chris@8
|
477
|
Chris@13
|
478 if (maxbin < 0) return fs;
|
Chris@13
|
479
|
Chris@13
|
480 double peakfreq = m_inputSampleRate / (maxbin + m_binFrom);
|
Chris@13
|
481 Hypothesis::Estimate e;
|
Chris@13
|
482 e.freq = peakfreq;
|
Chris@13
|
483 e.time = timestamp;
|
Chris@13
|
484
|
Chris@13
|
485 m_accepted.advanceTime();
|
Chris@16
|
486
|
Chris@13
|
487 for (int i = 0; i < m_possible.size(); ++i) {
|
Chris@13
|
488 m_possible[i].advanceTime();
|
Chris@13
|
489 }
|
Chris@13
|
490
|
Chris@16
|
491 if (!m_accepted.test(e)) {
|
Chris@16
|
492 int candidate = -1;
|
Chris@16
|
493 for (int i = 0; i < m_possible.size(); ++i) {
|
Chris@16
|
494 if (m_possible[i].test(e)) {
|
Chris@16
|
495 if (m_possible[i].getState() == Hypothesis::Satisfied) {
|
Chris@16
|
496 candidate = i;
|
Chris@16
|
497 }
|
Chris@16
|
498 break;
|
Chris@16
|
499 }
|
Chris@16
|
500 }
|
Chris@17
|
501
|
Chris@16
|
502 if (m_accepted.getState() == Hypothesis::Expired) {
|
Chris@16
|
503 m_accepted.addFeatures(fs[0]);
|
Chris@17
|
504 }
|
Chris@17
|
505
|
Chris@17
|
506 if (m_accepted.getState() == Hypothesis::Expired ||
|
Chris@17
|
507 m_accepted.getState() == Hypothesis::Rejected) {
|
Chris@16
|
508 if (candidate >= 0) {
|
Chris@16
|
509 m_accepted = m_possible[candidate];
|
Chris@16
|
510 } else {
|
Chris@16
|
511 m_accepted = Hypothesis();
|
Chris@16
|
512 }
|
Chris@16
|
513 }
|
Chris@13
|
514
|
Chris@17
|
515 std::cerr << "accepted length = " << m_accepted.getPendingLength()
|
Chris@17
|
516 << ", state = " << m_accepted.getState()
|
Chris@17
|
517 << ", hypothesis count = " << m_possible.size() << std::endl;
|
Chris@17
|
518
|
Chris@16
|
519 //!!! and also need to reap rejected/expired hypotheses from the list
|
Chris@16
|
520 }
|
Chris@16
|
521
|
Chris@13
|
522
|
Chris@13
|
523 /*
|
Chris@11
|
524 bool accepted = false;
|
Chris@11
|
525
|
Chris@11
|
526 if (maxbin >= 0) {
|
Chris@11
|
527 double pp = calculatePeakProportion(data, abstot, maxbin);
|
Chris@11
|
528 if (acceptPeak(maxbin, pp)) {
|
Chris@11
|
529 accepted = true;
|
Chris@11
|
530 } else {
|
Chris@11
|
531 // try a secondary peak
|
Chris@11
|
532 maxval = 0.0;
|
Chris@11
|
533 int secondbin = 0;
|
Chris@11
|
534 for (int i = 1; i < n-1; ++i) {
|
Chris@11
|
535 if (i != maxbin &&
|
Chris@11
|
536 data[i] > data[i-1] &&
|
Chris@11
|
537 data[i] > data[i+1] &&
|
Chris@11
|
538 data[i] > maxval) {
|
Chris@11
|
539 maxval = data[i];
|
Chris@11
|
540 secondbin = i;
|
Chris@11
|
541 }
|
Chris@11
|
542 }
|
Chris@11
|
543 double spp = calculatePeakProportion(data, abstot, secondbin);
|
Chris@11
|
544 if (acceptPeak(secondbin, spp)) {
|
Chris@11
|
545 maxbin = secondbin;
|
Chris@11
|
546 pp = spp;
|
Chris@11
|
547 accepted = true;
|
Chris@11
|
548 }
|
Chris@8
|
549 }
|
Chris@11
|
550 if (accepted) {
|
Chris@11
|
551 m_prevpeak = maxbin;
|
Chris@11
|
552 m_prevprop = pp;
|
Chris@8
|
553 }
|
Chris@8
|
554 }
|
Chris@13
|
555 */
|
Chris@8
|
556 // std::cerr << "peakProportion = " << peakProportion << std::endl;
|
Chris@8
|
557 // std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
|
Chris@9
|
558 // std::cerr << "bins = " << m_bins << std::endl;
|
Chris@8
|
559
|
Chris@11
|
560 // if (peakProportion >= (0.00006 * m_bins)) {
|
Chris@16
|
561 /*
|
Chris@11
|
562 if (accepted) {
|
Chris@8
|
563 Feature f;
|
Chris@8
|
564 f.hasTimestamp = true;
|
Chris@8
|
565 f.timestamp = timestamp;
|
Chris@8
|
566 f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
|
Chris@8
|
567 fs[0].push_back(f);
|
Chris@8
|
568 }
|
Chris@16
|
569 */
|
Chris@8
|
570 delete[] data;
|
Chris@8
|
571 return fs;
|
Chris@8
|
572 }
|
Chris@8
|
573
|
Chris@8
|
574 CepstrumPitchTracker::FeatureSet
|
Chris@8
|
575 CepstrumPitchTracker::getRemainingFeatures()
|
Chris@8
|
576 {
|
Chris@8
|
577 FeatureSet fs;
|
Chris@16
|
578 if (m_accepted.getState() != Hypothesis::New) {
|
Chris@16
|
579 m_accepted.addFeatures(fs[0]);
|
Chris@16
|
580 }
|
Chris@8
|
581 return fs;
|
Chris@8
|
582 }
|
Chris@8
|
583
|
Chris@8
|
584 void
|
Chris@8
|
585 CepstrumPitchTracker::fft(unsigned int n, bool inverse,
|
Chris@8
|
586 double *ri, double *ii, double *ro, double *io)
|
Chris@8
|
587 {
|
Chris@8
|
588 if (!ri || !ro || !io) return;
|
Chris@8
|
589
|
Chris@8
|
590 unsigned int bits;
|
Chris@8
|
591 unsigned int i, j, k, m;
|
Chris@8
|
592 unsigned int blockSize, blockEnd;
|
Chris@8
|
593
|
Chris@8
|
594 double tr, ti;
|
Chris@8
|
595
|
Chris@8
|
596 if (n < 2) return;
|
Chris@8
|
597 if (n & (n-1)) return;
|
Chris@8
|
598
|
Chris@8
|
599 double angle = 2.0 * M_PI;
|
Chris@8
|
600 if (inverse) angle = -angle;
|
Chris@8
|
601
|
Chris@8
|
602 for (i = 0; ; ++i) {
|
Chris@8
|
603 if (n & (1 << i)) {
|
Chris@8
|
604 bits = i;
|
Chris@8
|
605 break;
|
Chris@8
|
606 }
|
Chris@8
|
607 }
|
Chris@8
|
608
|
Chris@8
|
609 static unsigned int tableSize = 0;
|
Chris@8
|
610 static int *table = 0;
|
Chris@8
|
611
|
Chris@8
|
612 if (tableSize != n) {
|
Chris@8
|
613
|
Chris@8
|
614 delete[] table;
|
Chris@8
|
615
|
Chris@8
|
616 table = new int[n];
|
Chris@8
|
617
|
Chris@8
|
618 for (i = 0; i < n; ++i) {
|
Chris@8
|
619
|
Chris@8
|
620 m = i;
|
Chris@8
|
621
|
Chris@8
|
622 for (j = k = 0; j < bits; ++j) {
|
Chris@8
|
623 k = (k << 1) | (m & 1);
|
Chris@8
|
624 m >>= 1;
|
Chris@8
|
625 }
|
Chris@8
|
626
|
Chris@8
|
627 table[i] = k;
|
Chris@8
|
628 }
|
Chris@8
|
629
|
Chris@8
|
630 tableSize = n;
|
Chris@8
|
631 }
|
Chris@8
|
632
|
Chris@8
|
633 if (ii) {
|
Chris@8
|
634 for (i = 0; i < n; ++i) {
|
Chris@8
|
635 ro[table[i]] = ri[i];
|
Chris@8
|
636 io[table[i]] = ii[i];
|
Chris@8
|
637 }
|
Chris@8
|
638 } else {
|
Chris@8
|
639 for (i = 0; i < n; ++i) {
|
Chris@8
|
640 ro[table[i]] = ri[i];
|
Chris@8
|
641 io[table[i]] = 0.0;
|
Chris@8
|
642 }
|
Chris@8
|
643 }
|
Chris@8
|
644
|
Chris@8
|
645 blockEnd = 1;
|
Chris@8
|
646
|
Chris@8
|
647 for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
|
Chris@8
|
648
|
Chris@8
|
649 double delta = angle / (double)blockSize;
|
Chris@8
|
650 double sm2 = -sin(-2 * delta);
|
Chris@8
|
651 double sm1 = -sin(-delta);
|
Chris@8
|
652 double cm2 = cos(-2 * delta);
|
Chris@8
|
653 double cm1 = cos(-delta);
|
Chris@8
|
654 double w = 2 * cm1;
|
Chris@8
|
655 double ar[3], ai[3];
|
Chris@8
|
656
|
Chris@8
|
657 for (i = 0; i < n; i += blockSize) {
|
Chris@8
|
658
|
Chris@8
|
659 ar[2] = cm2;
|
Chris@8
|
660 ar[1] = cm1;
|
Chris@8
|
661
|
Chris@8
|
662 ai[2] = sm2;
|
Chris@8
|
663 ai[1] = sm1;
|
Chris@8
|
664
|
Chris@8
|
665 for (j = i, m = 0; m < blockEnd; j++, m++) {
|
Chris@8
|
666
|
Chris@8
|
667 ar[0] = w * ar[1] - ar[2];
|
Chris@8
|
668 ar[2] = ar[1];
|
Chris@8
|
669 ar[1] = ar[0];
|
Chris@8
|
670
|
Chris@8
|
671 ai[0] = w * ai[1] - ai[2];
|
Chris@8
|
672 ai[2] = ai[1];
|
Chris@8
|
673 ai[1] = ai[0];
|
Chris@8
|
674
|
Chris@8
|
675 k = j + blockEnd;
|
Chris@8
|
676 tr = ar[0] * ro[k] - ai[0] * io[k];
|
Chris@8
|
677 ti = ar[0] * io[k] + ai[0] * ro[k];
|
Chris@8
|
678
|
Chris@8
|
679 ro[k] = ro[j] - tr;
|
Chris@8
|
680 io[k] = io[j] - ti;
|
Chris@8
|
681
|
Chris@8
|
682 ro[j] += tr;
|
Chris@8
|
683 io[j] += ti;
|
Chris@8
|
684 }
|
Chris@8
|
685 }
|
Chris@8
|
686
|
Chris@8
|
687 blockEnd = blockSize;
|
Chris@8
|
688 }
|
Chris@8
|
689 }
|
Chris@8
|
690
|
Chris@8
|
691
|