# source:src/mathutils.h@acd97d1

feature/autosinkfeature/constantqfeature/pitchshiftfeature/pydocstringsfeature/timestretchpitchshiftsamplertimestretchyinfft+
Last change on this file since acd97d1 was acd97d1, checked in by Paul Brossier <piem@piem.org>, 7 years ago

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