1 | /* |
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2 | Copyright (C) 2003-2009 Paul Brossier <piem@aubio.org> |
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3 | |
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4 | This file is part of aubio. |
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5 | |
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6 | aubio is free software: you can redistribute it and/or modify |
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7 | it under the terms of the GNU General Public License as published by |
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8 | the Free Software Foundation, either version 3 of the License, or |
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9 | (at your option) any later version. |
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10 | |
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11 | aubio is distributed in the hope that it will be useful, |
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12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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14 | GNU General Public License for more details. |
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15 | |
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16 | You should have received a copy of the GNU General Public License |
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17 | along with aubio. If not, see <http://www.gnu.org/licenses/>. |
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18 | |
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19 | */ |
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20 | |
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21 | /** @file |
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22 | * various math functions |
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23 | */ |
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24 | |
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25 | #ifndef MATHUTILS_H |
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26 | #define MATHUTILS_H |
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27 | |
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28 | #include "fvec.h" |
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29 | #include "musicutils.h" |
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30 | |
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31 | #ifdef __cplusplus |
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32 | extern "C" { |
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33 | #endif |
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34 | |
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35 | /** compute the mean of a vector |
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36 | |
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37 | \param s vector to compute mean from |
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38 | |
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39 | \return the mean of v |
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40 | |
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41 | */ |
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42 | smpl_t fvec_mean (fvec_t * s); |
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43 | |
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44 | /** find the max of a vector |
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45 | |
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46 | \param s vector to get the max from |
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47 | |
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48 | \return the value of the minimum of v |
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49 | |
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50 | */ |
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51 | smpl_t fvec_max (fvec_t * s); |
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52 | |
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53 | /** find the min of a vector |
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54 | |
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55 | \param s vector to get the min from |
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56 | |
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57 | \return the value of the maximum of v |
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58 | |
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59 | */ |
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60 | smpl_t fvec_min (fvec_t * s); |
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61 | |
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62 | /** find the index of the min of a vector |
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63 | |
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64 | \param s vector to get the index from |
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65 | |
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66 | \return the index of the minimum element of v |
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67 | |
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68 | */ |
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69 | uint_t fvec_min_elem (fvec_t * s); |
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70 | |
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71 | /** find the index of the max of a vector |
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72 | |
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73 | \param s vector to get the index from |
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74 | |
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75 | \return the index of the maximum element of v |
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76 | |
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77 | */ |
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78 | uint_t fvec_max_elem (fvec_t * s); |
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79 | |
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80 | /** swap the left and right halves of a vector |
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81 | |
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82 | This function swaps the left part of the signal with the right part of the |
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83 | signal. Therefore |
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84 | |
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85 | \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$ |
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86 | |
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87 | becomes |
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88 | |
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89 | \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$ |
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90 | |
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91 | This operation, known as 'fftshift' in the Matlab Signal Processing Toolbox, |
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92 | can be used before computing the FFT to simplify the phase relationship of the |
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93 | resulting spectrum. See Amalia de Götzen's paper referred to above. |
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94 | |
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95 | */ |
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96 | void fvec_shift (fvec_t * v); |
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97 | |
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98 | /** compute the sum of all elements of a vector |
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99 | |
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100 | \param v vector to compute the sum of |
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101 | |
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102 | \return the sum of v |
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103 | |
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104 | */ |
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105 | smpl_t fvec_sum (fvec_t * v); |
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106 | |
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107 | /** compute the energy of a vector |
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108 | |
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109 | This function compute the sum of the squared elements of a vector. |
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110 | |
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111 | \param v vector to get the energy from |
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112 | |
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113 | \return the energy of v |
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114 | |
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115 | */ |
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116 | smpl_t fvec_local_energy (fvec_t * v); |
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117 | |
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118 | /** compute the High Frequency Content of a vector |
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119 | |
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120 | The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$. |
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121 | |
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122 | \param v vector to get the energy from |
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123 | |
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124 | \return the HFC of v |
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125 | |
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126 | */ |
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127 | smpl_t fvec_local_hfc (fvec_t * v); |
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128 | |
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129 | /** computes the p-norm of a vector |
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130 | |
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131 | Computes the p-norm of a vector for \f$ p = \alpha \f$ |
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132 | |
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133 | \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$ |
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134 | |
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135 | If p = 1, the result is the Manhattan distance. |
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136 | |
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137 | If p = 2, the result is the Euclidean distance. |
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138 | |
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139 | As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the |
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140 | input vector. |
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141 | |
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142 | References: |
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143 | |
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144 | - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on |
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145 | Wikipedia |
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146 | |
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147 | \param v vector to compute norm from |
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148 | \param p order of the computed norm |
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149 | |
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150 | \return the p-norm of v |
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151 | |
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152 | */ |
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153 | smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p); |
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154 | |
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155 | /** alpha normalisation |
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156 | |
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157 | This function divides all elements of a vector by the p-norm as computed by |
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158 | fvec_alpha_norm(). |
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159 | |
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160 | \param v vector to compute norm from |
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161 | \param p order of the computed norm |
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162 | |
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163 | */ |
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164 | void fvec_alpha_normalise (fvec_t * v, smpl_t p); |
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165 | |
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166 | /** add a constant to each elements of a vector |
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167 | |
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168 | \param v vector to add constant to |
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169 | \param c constant to add to v |
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170 | |
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171 | */ |
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172 | void fvec_add (fvec_t * v, smpl_t c); |
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173 | |
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174 | /** remove the minimum value of the vector to each elements |
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175 | |
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176 | \param v vector to remove minimum from |
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177 | |
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178 | */ |
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179 | void fvec_min_removal (fvec_t * v); |
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180 | |
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181 | /** compute moving median theshold of a vector |
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182 | |
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183 | This function computes the moving median threshold value of at the given |
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184 | position of a vector, taking the median amongs post elements before and up to |
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185 | pre elements after pos. |
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186 | |
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187 | \param v input vector |
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188 | \param tmp temporary vector of length post+1+pre |
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189 | \param post length of causal part to take before pos |
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190 | \param pre length of anti-causal part to take after pos |
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191 | \param pos index to compute threshold for |
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192 | |
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193 | \return moving median threshold value |
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194 | |
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195 | */ |
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196 | smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre, |
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197 | uint_t pos); |
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198 | |
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199 | /** apply adaptive threshold to a vector |
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200 | |
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201 | For each points at position p of an input vector, this function remove the |
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202 | moving median threshold computed at p. |
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203 | |
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204 | \param v input vector |
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205 | \param tmp temporary vector of length post+1+pre |
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206 | \param post length of causal part to take before pos |
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207 | \param pre length of anti-causal part to take after pos |
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208 | |
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209 | */ |
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210 | void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre); |
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211 | |
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212 | /** returns the median of a vector |
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213 | |
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214 | The QuickSelect routine is based on the algorithm described in "Numerical |
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215 | recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5, |
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216 | ISBN 0-521-43108-5 |
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217 | |
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218 | This implementation of the QuickSelect routine is based on Nicolas |
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219 | Devillard's implementation, available at http://ndevilla.free.fr/median/median/ |
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220 | and in the Public Domain. |
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221 | |
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222 | \param v vector to get median from |
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223 | |
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224 | \return the median of v |
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225 | |
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226 | */ |
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227 | smpl_t fvec_median (fvec_t * v); |
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228 | |
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229 | /** finds exact peak index by quadratic interpolation*/ |
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230 | smpl_t fvec_quadint (fvec_t * x, uint_t pos); |
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231 | |
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232 | /** Quadratic interpolation using Lagrange polynomial. |
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233 | |
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234 | Inspired from ``Comparison of interpolation algorithms in real-time sound |
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235 | processing'', Vladimir Arnost, |
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236 | |
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237 | \param s0,s1,s2 are 3 consecutive samples of a curve |
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238 | \param pf is the floating point index [0;2] |
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239 | |
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240 | \return s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); |
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241 | |
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242 | */ |
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243 | smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf); |
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244 | |
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245 | /** return 1 if v[p] is a peak and positive, 0 otherwise |
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246 | |
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247 | This function returns 1 if a peak is found at index p in the vector v. The |
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248 | peak is defined as follows: |
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249 | |
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250 | - v[p] is positive |
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251 | - v[p-1] < v[p] |
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252 | - v[p] > v[p+1] |
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253 | |
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254 | \param v input vector |
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255 | \param p position of supposed for peak |
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256 | |
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257 | \return 1 if a peak is found, 0 otherwise |
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258 | |
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259 | */ |
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260 | uint_t fvec_peakpick (fvec_t * v, uint_t p); |
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261 | |
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262 | /** return 1 if a is a power of 2, 0 otherwise */ |
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263 | uint_t aubio_is_power_of_two(uint_t a); |
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264 | |
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265 | /** return the next power of power of 2 greater than a */ |
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266 | uint_t aubio_next_power_of_two(uint_t a); |
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267 | |
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268 | /** compute normalised autocorrelation function |
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269 | |
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270 | \param input vector to compute autocorrelation from |
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271 | \param output vector to store autocorrelation function to |
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272 | |
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273 | */ |
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274 | void aubio_autocorr (fvec_t * input, fvec_t * output); |
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275 | |
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276 | #ifdef __cplusplus |
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277 | } |
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278 | #endif |
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279 | |
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280 | #endif |
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281 | |
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