1 | /* |
---|
2 | Copyright (C) 2003-2009 Paul Brossier <piem@aubio.org> |
---|
3 | |
---|
4 | This file is part of aubio. |
---|
5 | |
---|
6 | aubio is free software: you can redistribute it and/or modify |
---|
7 | it under the terms of the GNU General Public License as published by |
---|
8 | the Free Software Foundation, either version 3 of the License, or |
---|
9 | (at your option) any later version. |
---|
10 | |
---|
11 | aubio is distributed in the hope that it will be useful, |
---|
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
---|
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
---|
14 | GNU General Public License for more details. |
---|
15 | |
---|
16 | You should have received a copy of the GNU General Public License |
---|
17 | along with aubio. If not, see <http://www.gnu.org/licenses/>. |
---|
18 | |
---|
19 | */ |
---|
20 | |
---|
21 | /** @file |
---|
22 | * various math functions |
---|
23 | */ |
---|
24 | |
---|
25 | #ifndef MATHUTILS_H |
---|
26 | #define MATHUTILS_H |
---|
27 | |
---|
28 | #include "fvec.h" |
---|
29 | #include "musicutils.h" |
---|
30 | |
---|
31 | #ifdef __cplusplus |
---|
32 | extern "C" { |
---|
33 | #endif |
---|
34 | |
---|
35 | /** compute the mean of a vector |
---|
36 | |
---|
37 | \param s vector to compute mean from |
---|
38 | |
---|
39 | \return the mean of v |
---|
40 | |
---|
41 | */ |
---|
42 | smpl_t fvec_mean (fvec_t * s); |
---|
43 | |
---|
44 | /** find the max of a vector |
---|
45 | |
---|
46 | \param s vector to get the max from |
---|
47 | |
---|
48 | \return the value of the minimum of v |
---|
49 | |
---|
50 | */ |
---|
51 | smpl_t fvec_max (fvec_t * s); |
---|
52 | |
---|
53 | /** find the min of a vector |
---|
54 | |
---|
55 | \param s vector to get the min from |
---|
56 | |
---|
57 | \return the value of the maximum of v |
---|
58 | |
---|
59 | */ |
---|
60 | smpl_t fvec_min (fvec_t * s); |
---|
61 | |
---|
62 | /** find the index of the min of a vector |
---|
63 | |
---|
64 | \param s vector to get the index from |
---|
65 | |
---|
66 | \return the index of the minimum element of v |
---|
67 | |
---|
68 | */ |
---|
69 | uint_t fvec_min_elem (fvec_t * s); |
---|
70 | |
---|
71 | /** find the index of the max of a vector |
---|
72 | |
---|
73 | \param s vector to get the index from |
---|
74 | |
---|
75 | \return the index of the maximum element of v |
---|
76 | |
---|
77 | */ |
---|
78 | uint_t fvec_max_elem (fvec_t * s); |
---|
79 | |
---|
80 | /** swap the left and right halves of a vector |
---|
81 | |
---|
82 | This function swaps the left part of the signal with the right part of the |
---|
83 | signal. Therefore |
---|
84 | |
---|
85 | \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$ |
---|
86 | |
---|
87 | becomes |
---|
88 | |
---|
89 | \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$ |
---|
90 | |
---|
91 | This operation, known as 'fftshift' in the Matlab Signal Processing Toolbox, |
---|
92 | can be used before computing the FFT to simplify the phase relationship of the |
---|
93 | resulting spectrum. See Amalia de Götzen's paper referred to above. |
---|
94 | |
---|
95 | */ |
---|
96 | void fvec_shift (fvec_t * v); |
---|
97 | |
---|
98 | /** compute the sum of all elements of a vector |
---|
99 | |
---|
100 | \param v vector to compute the sum of |
---|
101 | |
---|
102 | \return the sum of v |
---|
103 | |
---|
104 | */ |
---|
105 | smpl_t fvec_sum (fvec_t * v); |
---|
106 | |
---|
107 | /** compute the energy of a vector |
---|
108 | |
---|
109 | This function compute the sum of the squared elements of a vector, normalised |
---|
110 | by its length. |
---|
111 | |
---|
112 | \param v vector to get the energy from |
---|
113 | |
---|
114 | \return the energy of v |
---|
115 | |
---|
116 | */ |
---|
117 | smpl_t fvec_local_energy (fvec_t * v); |
---|
118 | |
---|
119 | /** compute the High Frequency Content of a vector |
---|
120 | |
---|
121 | The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$. |
---|
122 | |
---|
123 | \param v vector to get the energy from |
---|
124 | |
---|
125 | \return the HFC of v |
---|
126 | |
---|
127 | */ |
---|
128 | smpl_t fvec_local_hfc (fvec_t * v); |
---|
129 | |
---|
130 | /** computes the p-norm of a vector |
---|
131 | |
---|
132 | Computes the p-norm of a vector for \f$ p = \alpha \f$ |
---|
133 | |
---|
134 | \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$ |
---|
135 | |
---|
136 | If p = 1, the result is the Manhattan distance. |
---|
137 | |
---|
138 | If p = 2, the result is the Euclidean distance. |
---|
139 | |
---|
140 | As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the |
---|
141 | input vector. |
---|
142 | |
---|
143 | References: |
---|
144 | |
---|
145 | - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on |
---|
146 | Wikipedia |
---|
147 | |
---|
148 | \param v vector to compute norm from |
---|
149 | \param p order of the computed norm |
---|
150 | |
---|
151 | \return the p-norm of v |
---|
152 | |
---|
153 | */ |
---|
154 | smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p); |
---|
155 | |
---|
156 | /** alpha normalisation |
---|
157 | |
---|
158 | This function divides all elements of a vector by the p-norm as computed by |
---|
159 | fvec_alpha_norm(). |
---|
160 | |
---|
161 | \param v vector to compute norm from |
---|
162 | \param p order of the computed norm |
---|
163 | |
---|
164 | */ |
---|
165 | void fvec_alpha_normalise (fvec_t * v, smpl_t p); |
---|
166 | |
---|
167 | /** add a constant to each elements of a vector |
---|
168 | |
---|
169 | \param v vector to add constant to |
---|
170 | \param c constant to add to v |
---|
171 | |
---|
172 | */ |
---|
173 | void fvec_add (fvec_t * v, smpl_t c); |
---|
174 | |
---|
175 | /** remove the minimum value of the vector to each elements |
---|
176 | |
---|
177 | \param v vector to remove minimum from |
---|
178 | |
---|
179 | */ |
---|
180 | void fvec_min_removal (fvec_t * v); |
---|
181 | |
---|
182 | /** compute moving median theshold of a vector |
---|
183 | |
---|
184 | This function computes the moving median threshold value of at the given |
---|
185 | position of a vector, taking the median amongs post elements before and up to |
---|
186 | pre elements after pos. |
---|
187 | |
---|
188 | \param v input vector |
---|
189 | \param tmp temporary vector of length post+1+pre |
---|
190 | \param post length of causal part to take before pos |
---|
191 | \param pre length of anti-causal part to take after pos |
---|
192 | \param pos index to compute threshold for |
---|
193 | |
---|
194 | \return moving median threshold value |
---|
195 | |
---|
196 | */ |
---|
197 | smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre, |
---|
198 | uint_t pos); |
---|
199 | |
---|
200 | /** apply adaptive threshold to a vector |
---|
201 | |
---|
202 | For each points at position p of an input vector, this function remove the |
---|
203 | moving median threshold computed at p. |
---|
204 | |
---|
205 | \param v input vector |
---|
206 | \param tmp temporary vector of length post+1+pre |
---|
207 | \param post length of causal part to take before pos |
---|
208 | \param pre length of anti-causal part to take after pos |
---|
209 | |
---|
210 | */ |
---|
211 | void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre); |
---|
212 | |
---|
213 | /** returns the median of a vector |
---|
214 | |
---|
215 | The QuickSelect routine is based on the algorithm described in "Numerical |
---|
216 | recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5, |
---|
217 | ISBN 0-521-43108-5 |
---|
218 | |
---|
219 | This implementation of the QuickSelect routine is based on Nicolas |
---|
220 | Devillard's implementation, available at http://ndevilla.free.fr/median/median/ |
---|
221 | and in the Public Domain. |
---|
222 | |
---|
223 | \param v vector to get median from |
---|
224 | |
---|
225 | \return the median of v |
---|
226 | |
---|
227 | */ |
---|
228 | smpl_t fvec_median (fvec_t * v); |
---|
229 | |
---|
230 | /** finds exact peak index by quadratic interpolation*/ |
---|
231 | smpl_t fvec_quadint (fvec_t * x, uint_t pos); |
---|
232 | |
---|
233 | /** Quadratic interpolation using Lagrange polynomial. |
---|
234 | |
---|
235 | Inspired from ``Comparison of interpolation algorithms in real-time sound |
---|
236 | processing'', Vladimir Arnost, |
---|
237 | |
---|
238 | \param s0,s1,s2 are 3 consecutive samples of a curve |
---|
239 | \param pf is the floating point index [0;2] |
---|
240 | |
---|
241 | \return s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); |
---|
242 | |
---|
243 | */ |
---|
244 | smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf); |
---|
245 | |
---|
246 | /** return 1 if v[p] is a peak and positive, 0 otherwise |
---|
247 | |
---|
248 | This function returns 1 if a peak is found at index p in the vector v. The |
---|
249 | peak is defined as follows: |
---|
250 | |
---|
251 | - v[p] is positive |
---|
252 | - v[p-1] < v[p] |
---|
253 | - v[p] > v[p+1] |
---|
254 | |
---|
255 | \param v input vector |
---|
256 | \param p position of supposed for peak |
---|
257 | |
---|
258 | \return 1 if a peak is found, 0 otherwise |
---|
259 | |
---|
260 | */ |
---|
261 | uint_t fvec_peakpick (fvec_t * v, uint_t p); |
---|
262 | |
---|
263 | /** return 1 if a is a power of 2, 0 otherwise */ |
---|
264 | uint_t aubio_is_power_of_two(uint_t a); |
---|
265 | |
---|
266 | /** return the next power of power of 2 greater than a */ |
---|
267 | uint_t aubio_next_power_of_two(uint_t a); |
---|
268 | |
---|
269 | /** compute normalised autocorrelation function |
---|
270 | |
---|
271 | \param input vector to compute autocorrelation from |
---|
272 | \param output vector to store autocorrelation function to |
---|
273 | |
---|
274 | */ |
---|
275 | void aubio_autocorr (fvec_t * input, fvec_t * output); |
---|
276 | |
---|
277 | #ifdef __cplusplus |
---|
278 | } |
---|
279 | #endif |
---|
280 | |
---|
281 | #endif |
---|
282 | |
---|