source: src/mathutils.h @ 6f42c16

feature/autosinkfeature/constantqfeature/pitchshiftfeature/pydocstringsfeature/timestretchpitchshiftsamplertimestretchyinfft+
Last change on this file since 6f42c16 was 6f42c16, checked in by Paul Brossier <piem@piem.org>, 3 years ago

src/: change c header identifiers (see #35)

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1/*
2  Copyright (C) 2003-2015 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/** swap the left and right halves of a vector
103
104  This function swaps the left part of the signal with the right part of the
105signal. Therefore
106
107  \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$
108
109  becomes
110
111  \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$
112
113  This operation, known as 'ifftshift' in the Matlab Signal Processing Toolbox,
114can be used after computing the inverse FFT to simplify the phase relationship
115of the resulting spectrum. See Amalia de Götzen's paper referred to above.
116
117*/
118void fvec_ishift (fvec_t * v);
119
120/** compute the sum of all elements of a vector
121
122  \param v vector to compute the sum of
123
124  \return the sum of v
125
126*/
127smpl_t fvec_sum (fvec_t * v);
128
129/** compute the High Frequency Content of a vector
130
131  The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$.
132
133  \param v vector to get the energy from
134
135  \return the HFC of v
136
137*/
138smpl_t fvec_local_hfc (fvec_t * v);
139
140/** computes the p-norm of a vector
141
142  Computes the p-norm of a vector for \f$ p = \alpha \f$
143
144  \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$
145
146  If p = 1, the result is the Manhattan distance.
147
148  If p = 2, the result is the Euclidean distance.
149
150  As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the
151input vector.
152
153  References:
154
155    - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on
156  Wikipedia
157
158  \param v vector to compute norm from
159  \param p order of the computed norm
160
161  \return the p-norm of v
162
163*/
164smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p);
165
166/**  alpha normalisation
167
168  This function divides all elements of a vector by the p-norm as computed by
169fvec_alpha_norm().
170
171  \param v vector to compute norm from
172  \param p order of the computed norm
173
174*/
175void fvec_alpha_normalise (fvec_t * v, smpl_t p);
176
177/** add a constant to each elements of a vector
178
179  \param v vector to add constant to
180  \param c constant to add to v
181
182*/
183void fvec_add (fvec_t * v, smpl_t c);
184
185/** remove the minimum value of the vector to each elements
186
187  \param v vector to remove minimum from
188
189*/
190void fvec_min_removal (fvec_t * v);
191
192/** compute moving median threshold of a vector
193
194  This function computes the moving median threshold value of at the given
195position of a vector, taking the median among post elements before and up to
196pre elements after pos.
197
198  \param v input vector
199  \param tmp temporary vector of length post+1+pre
200  \param post length of causal part to take before pos
201  \param pre length of anti-causal part to take after pos
202  \param pos index to compute threshold for
203
204  \return moving median threshold value
205
206*/
207smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
208    uint_t pos);
209
210/** apply adaptive threshold to a vector
211
212  For each points at position p of an input vector, this function remove the
213moving median threshold computed at p.
214
215  \param v input vector
216  \param tmp temporary vector of length post+1+pre
217  \param post length of causal part to take before pos
218  \param pre length of anti-causal part to take after pos
219
220*/
221void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);
222
223/** returns the median of a vector
224
225  The QuickSelect routine is based on the algorithm described in "Numerical
226recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
227ISBN 0-521-43108-5
228
229  This implementation of the QuickSelect routine is based on Nicolas
230Devillard's implementation, available at http://ndevilla.free.fr/median/median/
231and in the Public Domain.
232
233  \param v vector to get median from
234
235  \return the median of v
236
237*/
238smpl_t fvec_median (fvec_t * v);
239
240/** finds exact peak index by quadratic interpolation
241
242  See [Quadratic Interpolation of Spectral
243  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
244  by Julius O. Smith III
245
246  \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$
247
248  \param x vector to get the interpolated peak position from
249  \param p index of the peak in vector `x`
250  \return \f$ p + p_{frac} \f$ exact peak position of interpolated maximum or minimum
251
252*/
253smpl_t fvec_quadratic_peak_pos (const fvec_t * x, uint_t p);
254
255/** finds magnitude of peak by quadratic interpolation
256
257  See [Quadratic Interpolation of Spectral
258  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
259  by Julius O. Smith III
260
261  \param x vector to get the magnitude of the interpolated peak position from
262  \param p index of the peak in vector `x`
263  \return magnitude of interpolated peak
264
265*/
266smpl_t fvec_quadratic_peak_mag (fvec_t * x, smpl_t p);
267
268/** Quadratic interpolation using Lagrange polynomial.
269
270  Inspired from ``Comparison of interpolation algorithms in real-time sound
271processing'', Vladimir Arnost,
272
273  \param s0,s1,s2 are 3 consecutive samples of a curve
274  \param pf is the floating point index [0;2]
275
276  \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$
277
278*/
279smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);
280
281/** return 1 if v[p] is a peak and positive, 0 otherwise
282
283  This function returns 1 if a peak is found at index p in the vector v. The
284peak is defined as follows:
285
286  - v[p] is positive
287  - v[p-1] < v[p]
288  - v[p] > v[p+1]
289
290  \param v input vector
291  \param p position of supposed for peak
292
293  \return 1 if a peak is found, 0 otherwise
294
295*/
296uint_t fvec_peakpick (const fvec_t * v, uint_t p);
297
298/** return 1 if a is a power of 2, 0 otherwise */
299uint_t aubio_is_power_of_two(uint_t a);
300
301/** return the next power of power of 2 greater than a */
302uint_t aubio_next_power_of_two(uint_t a);
303
304/** compute normalised autocorrelation function
305
306  \param input vector to compute autocorrelation from
307  \param output vector to store autocorrelation function to
308
309*/
310void aubio_autocorr (const fvec_t * input, fvec_t * output);
311
312#ifdef __cplusplus
313}
314#endif
315
316#endif /* AUBIO_MATHUTILS_H */
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