source: src/mathutils.h @ d4791e5

feature/autosinkfeature/cnnfeature/cnn_orgfeature/constantqfeature/crepefeature/crepe_orgfeature/pitchshiftfeature/pydocstringsfeature/timestretchfix/ffmpeg5pitchshiftsamplertimestretchyinfft+
Last change on this file since d4791e5 was b235c0e, checked in by Paul Brossier <piem@piem.org>, 11 years ago

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1/*
2  Copyright (C) 2003-2013 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
23  Various math functions
24
25  \example test-mathutils.c
26  \example test-mathutils-window.c
27
28 */
29
30#ifndef _AUBIO_MATHUTILS_H
31#define _AUBIO_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[0], a[1], ..., 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[0], a[1], ..., 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 High Frequency Content of a vector
112
113  The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$.
114 
115  \param v vector to get the energy from
116
117  \return the HFC of v
118 
119*/
120smpl_t fvec_local_hfc (fvec_t * v);
121
122/** computes the p-norm of a vector
123 
124  Computes the p-norm of a vector for \f$ p = \alpha \f$
125
126  \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$
127 
128  If p = 1, the result is the Manhattan distance.
129
130  If p = 2, the result is the Euclidean distance.
131
132  As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the
133input vector.
134
135  References:
136 
137    - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on
138  Wikipedia
139
140  \param v vector to compute norm from
141  \param p order of the computed norm
142
143  \return the p-norm of v
144 
145*/
146smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p);
147
148/**  alpha normalisation
149
150  This function divides all elements of a vector by the p-norm as computed by
151fvec_alpha_norm().
152
153  \param v vector to compute norm from
154  \param p order of the computed norm
155
156*/
157void fvec_alpha_normalise (fvec_t * v, smpl_t p);
158
159/** add a constant to each elements of a vector
160
161  \param v vector to add constant to
162  \param c constant to add to v
163
164*/
165void fvec_add (fvec_t * v, smpl_t c);
166
167/** remove the minimum value of the vector to each elements
168 
169  \param v vector to remove minimum from
170
171*/
172void fvec_min_removal (fvec_t * v);
173
174/** compute moving median threshold of a vector
175
176  This function computes the moving median threshold value of at the given
177position of a vector, taking the median among post elements before and up to
178pre elements after pos.
179 
180  \param v input vector
181  \param tmp temporary vector of length post+1+pre
182  \param post length of causal part to take before pos
183  \param pre length of anti-causal part to take after pos
184  \param pos index to compute threshold for
185
186  \return moving median threshold value
187
188*/
189smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
190    uint_t pos);
191
192/** apply adaptive threshold to a vector
193
194  For each points at position p of an input vector, this function remove the
195moving median threshold computed at p.
196
197  \param v input vector
198  \param tmp temporary vector of length post+1+pre
199  \param post length of causal part to take before pos
200  \param pre length of anti-causal part to take after pos
201
202*/
203void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);
204
205/** returns the median of a vector
206
207  The QuickSelect routine is based on the algorithm described in "Numerical
208recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
209ISBN 0-521-43108-5
210
211  This implementation of the QuickSelect routine is based on Nicolas
212Devillard's implementation, available at http://ndevilla.free.fr/median/median/
213and in the Public Domain.
214
215  \param v vector to get median from
216
217  \return the median of v
218 
219*/
220smpl_t fvec_median (fvec_t * v);
221
222/** finds exact peak index by quadratic interpolation
223
224  See [Quadratic Interpolation of Spectral
225  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
226  by Julius O. Smith III
227
228  \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$
229
230  \param x vector to get the interpolated peak position from
231  \param p index of the peak in vector `x`
232  \return \f$ p + p_{frac} \f$ exact peak position of interpolated maximum or minimum
233
234*/
235smpl_t fvec_quadratic_peak_pos (fvec_t * x, uint_t p);
236
237/** Quadratic interpolation using Lagrange polynomial.
238 
239  Inspired from ``Comparison of interpolation algorithms in real-time sound
240processing'', Vladimir Arnost,
241 
242  \param s0,s1,s2 are 3 consecutive samples of a curve
243  \param pf is the floating point index [0;2]
244 
245  \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$
246
247*/
248smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);
249
250/** return 1 if v[p] is a peak and positive, 0 otherwise
251
252  This function returns 1 if a peak is found at index p in the vector v. The
253peak is defined as follows:
254
255  - v[p] is positive
256  - v[p-1] < v[p]
257  - v[p] > v[p+1]
258
259  \param v input vector
260  \param p position of supposed for peak
261
262  \return 1 if a peak is found, 0 otherwise
263
264*/
265uint_t fvec_peakpick (fvec_t * v, uint_t p);
266
267/** return 1 if a is a power of 2, 0 otherwise */
268uint_t aubio_is_power_of_two(uint_t a);
269
270/** return the next power of power of 2 greater than a */
271uint_t aubio_next_power_of_two(uint_t a);
272
273/** compute normalised autocorrelation function
274
275  \param input vector to compute autocorrelation from
276  \param output vector to store autocorrelation function to
277
278*/
279void aubio_autocorr (fvec_t * input, fvec_t * output);
280
281#ifdef __cplusplus
282}
283#endif
284
285#endif /* _AUBIO_MATHUTILS_H */
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