1 | /* |
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2 | Copyright (C) 2003-2015 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 | |
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23 | Various math functions |
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24 | |
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25 | \example test-mathutils.c |
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26 | \example test-mathutils-window.c |
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27 | |
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28 | */ |
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29 | |
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30 | #ifndef AUBIO_MATHUTILS_H |
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31 | #define AUBIO_MATHUTILS_H |
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32 | |
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33 | #include "fvec.h" |
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34 | #include "musicutils.h" |
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35 | |
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36 | #ifdef __cplusplus |
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37 | extern "C" { |
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38 | #endif |
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39 | |
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40 | /** compute the mean of a vector |
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41 | |
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42 | \param s vector to compute mean from |
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43 | \return the mean of `v` |
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44 | |
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45 | */ |
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46 | smpl_t fvec_mean (fvec_t * s); |
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47 | |
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48 | /** find the max of a vector |
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49 | |
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50 | \param s vector to get the max from |
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51 | |
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52 | \return the value of the minimum of v |
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53 | |
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54 | */ |
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55 | smpl_t fvec_max (fvec_t * s); |
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56 | |
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57 | /** find the min of a vector |
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58 | |
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59 | \param s vector to get the min from |
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60 | |
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61 | \return the value of the maximum of v |
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62 | |
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63 | */ |
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64 | smpl_t fvec_min (fvec_t * s); |
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65 | |
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66 | /** find the index of the min of a vector |
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67 | |
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68 | \param s vector to get the index from |
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69 | |
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70 | \return the index of the minimum element of v |
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71 | |
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72 | */ |
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73 | uint_t fvec_min_elem (fvec_t * s); |
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74 | |
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75 | /** find the index of the max of a vector |
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76 | |
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77 | \param s vector to get the index from |
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78 | |
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79 | \return the index of the maximum element of v |
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80 | |
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81 | */ |
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82 | uint_t fvec_max_elem (fvec_t * s); |
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83 | |
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84 | /** swap the left and right halves of a vector |
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85 | |
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86 | This function swaps the left part of the signal with the right part of the |
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87 | signal. Therefore |
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88 | |
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89 | \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$ |
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90 | |
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91 | becomes |
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92 | |
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93 | \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$ |
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94 | |
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95 | This operation, known as 'fftshift' in the Matlab Signal Processing Toolbox, |
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96 | can be used before computing the FFT to simplify the phase relationship of the |
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97 | resulting spectrum. See Amalia de Götzen's paper referred to above. |
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98 | |
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99 | */ |
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100 | void fvec_shift (fvec_t * v); |
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101 | |
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102 | /** swap the left and right halves of a vector |
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103 | |
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104 | This function swaps the left part of the signal with the right part of the |
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105 | signal. Therefore |
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106 | |
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107 | \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$ |
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108 | |
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109 | becomes |
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110 | |
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111 | \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$ |
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112 | |
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113 | This operation, known as 'ifftshift' in the Matlab Signal Processing Toolbox, |
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114 | can be used after computing the inverse FFT to simplify the phase relationship |
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115 | of the resulting spectrum. See Amalia de Götzen's paper referred to above. |
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116 | |
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117 | */ |
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118 | void fvec_ishift (fvec_t * v); |
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119 | |
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120 | /** push a new element to the end of a vector, erasing the first element and |
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121 | * sliding all others |
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122 | |
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123 | \param in vector to push to |
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124 | \param new_elem new_element to add at the end of the vector |
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125 | |
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126 | In numpy words, this is equivalent to: in = np.concatenate([in, [new_elem]])[1:] |
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127 | |
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128 | */ |
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129 | void fvec_push(fvec_t *in, smpl_t new_elem); |
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130 | |
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131 | /** compute the sum of all elements of a vector |
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132 | |
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133 | \param v vector to compute the sum of |
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134 | |
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135 | \return the sum of v |
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136 | |
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137 | */ |
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138 | smpl_t fvec_sum (fvec_t * v); |
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139 | |
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140 | /** compute the High Frequency Content of a vector |
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141 | |
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142 | The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$. |
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143 | |
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144 | \param v vector to get the energy from |
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145 | |
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146 | \return the HFC of v |
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147 | |
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148 | */ |
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149 | smpl_t fvec_local_hfc (fvec_t * v); |
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150 | |
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151 | /** computes the p-norm of a vector |
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152 | |
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153 | Computes the p-norm of a vector for \f$ p = \alpha \f$ |
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154 | |
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155 | \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$ |
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156 | |
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157 | If p = 1, the result is the Manhattan distance. |
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158 | |
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159 | If p = 2, the result is the Euclidean distance. |
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160 | |
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161 | As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the |
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162 | input vector. |
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163 | |
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164 | References: |
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165 | |
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166 | - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on |
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167 | Wikipedia |
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168 | |
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169 | \param v vector to compute norm from |
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170 | \param p order of the computed norm |
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171 | |
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172 | \return the p-norm of v |
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173 | |
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174 | */ |
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175 | smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p); |
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176 | |
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177 | /** alpha normalisation |
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178 | |
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179 | This function divides all elements of a vector by the p-norm as computed by |
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180 | fvec_alpha_norm(). |
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181 | |
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182 | \param v vector to compute norm from |
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183 | \param p order of the computed norm |
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184 | |
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185 | */ |
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186 | void fvec_alpha_normalise (fvec_t * v, smpl_t p); |
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187 | |
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188 | /** add a constant to each elements of a vector |
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189 | |
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190 | \param v vector to add constant to |
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191 | \param c constant to add to v |
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192 | |
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193 | */ |
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194 | void fvec_add (fvec_t * v, smpl_t c); |
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195 | |
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196 | /** multiply each elements of a vector by a scalar |
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197 | |
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198 | \param v vector to add constant to |
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199 | \param s constant to scale v with |
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200 | |
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201 | */ |
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202 | void fvec_mul (fvec_t * v, smpl_t s); |
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203 | |
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204 | /** remove the minimum value of the vector to each elements |
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205 | |
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206 | \param v vector to remove minimum from |
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207 | |
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208 | */ |
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209 | void fvec_min_removal (fvec_t * v); |
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210 | |
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211 | /** compute moving median threshold of a vector |
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212 | |
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213 | This function computes the moving median threshold value of at the given |
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214 | position of a vector, taking the median among post elements before and up to |
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215 | pre elements after pos. |
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216 | |
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217 | \param v input vector |
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218 | \param tmp temporary vector of length post+1+pre |
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219 | \param post length of causal part to take before pos |
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220 | \param pre length of anti-causal part to take after pos |
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221 | \param pos index to compute threshold for |
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222 | |
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223 | \return moving median threshold value |
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224 | |
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225 | */ |
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226 | smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre, |
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227 | uint_t pos); |
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228 | |
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229 | /** apply adaptive threshold to a vector |
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230 | |
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231 | For each points at position p of an input vector, this function remove the |
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232 | moving median threshold computed at p. |
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233 | |
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234 | \param v input vector |
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235 | \param tmp temporary vector of length post+1+pre |
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236 | \param post length of causal part to take before pos |
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237 | \param pre length of anti-causal part to take after pos |
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238 | |
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239 | */ |
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240 | void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre); |
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241 | |
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242 | /** returns the median of a vector |
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243 | |
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244 | The QuickSelect routine is based on the algorithm described in "Numerical |
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245 | recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5, |
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246 | ISBN 0-521-43108-5 |
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247 | |
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248 | This implementation of the QuickSelect routine is based on Nicolas |
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249 | Devillard's implementation, available at http://ndevilla.free.fr/median/median/ |
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250 | and in the Public Domain. |
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251 | |
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252 | \param v vector to get median from |
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253 | |
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254 | \return the median of v |
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255 | |
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256 | */ |
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257 | smpl_t fvec_median (fvec_t * v); |
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258 | |
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259 | /** finds exact peak index by quadratic interpolation |
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260 | |
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261 | See [Quadratic Interpolation of Spectral |
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262 | Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html), |
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263 | by Julius O. Smith III |
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264 | |
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265 | \f$ p_{frac} = \frac{1}{2} \frac {x[p-1] - x[p+1]} {x[p-1] - 2 x[p] + x[p+1]} \in [ -.5, .5] \f$ |
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266 | |
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267 | \param x vector to get the interpolated peak position from |
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268 | \param p index of the peak in vector `x` |
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269 | \return \f$ p + p_{frac} \f$ exact peak position of interpolated maximum or minimum |
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270 | |
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271 | */ |
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272 | smpl_t fvec_quadratic_peak_pos (const fvec_t * x, uint_t p); |
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273 | |
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274 | /** finds magnitude of peak by quadratic interpolation |
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275 | |
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276 | See [Quadratic Interpolation of Spectral |
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277 | Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html), |
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278 | by Julius O. Smith III |
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279 | |
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280 | \param x vector to get the magnitude of the interpolated peak position from |
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281 | \param p index of the peak in vector `x` |
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282 | \return magnitude of interpolated peak |
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283 | |
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284 | */ |
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285 | smpl_t fvec_quadratic_peak_mag (fvec_t * x, smpl_t p); |
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286 | |
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287 | /** Quadratic interpolation using Lagrange polynomial. |
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288 | |
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289 | Inspired from ``Comparison of interpolation algorithms in real-time sound |
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290 | processing'', Vladimir Arnost, |
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291 | |
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292 | \param s0,s1,s2 are 3 consecutive samples of a curve |
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293 | \param pf is the floating point index [0;2] |
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294 | |
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295 | \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$ |
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296 | |
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297 | */ |
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298 | smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf); |
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299 | |
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300 | /** return 1 if v[p] is a peak and positive, 0 otherwise |
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301 | |
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302 | This function returns 1 if a peak is found at index p in the vector v. The |
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303 | peak is defined as follows: |
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304 | |
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305 | - v[p] is positive |
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306 | - v[p-1] < v[p] |
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307 | - v[p] > v[p+1] |
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308 | |
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309 | \param v input vector |
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310 | \param p position of supposed for peak |
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311 | |
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312 | \return 1 if a peak is found, 0 otherwise |
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313 | |
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314 | */ |
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315 | uint_t fvec_peakpick (const fvec_t * v, uint_t p); |
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316 | |
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317 | /** return 1 if a is a power of 2, 0 otherwise */ |
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318 | uint_t aubio_is_power_of_two(uint_t a); |
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319 | |
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320 | /** return the next power of power of 2 greater than a */ |
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321 | uint_t aubio_next_power_of_two(uint_t a); |
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322 | |
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323 | /** return the log2 factor of the given power of 2 value a */ |
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324 | uint_t aubio_power_of_two_order(uint_t a); |
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325 | |
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326 | /** compute normalised autocorrelation function |
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327 | |
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328 | \param input vector to compute autocorrelation from |
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329 | \param output vector to store autocorrelation function to |
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330 | |
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331 | */ |
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332 | void aubio_autocorr (const fvec_t * input, fvec_t * output); |
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333 | |
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334 | #ifdef __cplusplus |
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335 | } |
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336 | #endif |
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337 | |
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338 | #endif /* AUBIO_MATHUTILS_H */ |
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