2 Copyright (C) 2003-2014 Paul Brossier <piem@aubio.org>
4 This file is part of aubio.
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.
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.
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/>.
23 Various math functions
25 \example test-mathutils.c
26 \example test-mathutils-window.c
30 #ifndef _AUBIO_MATHUTILS_H
31 #define _AUBIO_MATHUTILS_H
34 #include "musicutils.h"
40 /** compute the mean of a vector
42 \param s vector to compute mean from
43 \return the mean of `v`
46 smpl_t fvec_mean (fvec_t * s);
48 /** find the max of a vector
50 \param s vector to get the max from
52 \return the value of the minimum of v
55 smpl_t fvec_max (fvec_t * s);
57 /** find the min of a vector
59 \param s vector to get the min from
61 \return the value of the maximum of v
64 smpl_t fvec_min (fvec_t * s);
66 /** find the index of the min of a vector
68 \param s vector to get the index from
70 \return the index of the minimum element of v
73 uint_t fvec_min_elem (fvec_t * s);
75 /** find the index of the max of a vector
77 \param s vector to get the index from
79 \return the index of the maximum element of v
82 uint_t fvec_max_elem (fvec_t * s);
84 /** swap the left and right halves of a vector
86 This function swaps the left part of the signal with the right part of the
89 \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$
93 \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$
95 This operation, known as 'fftshift' in the Matlab Signal Processing Toolbox,
96 can be used before computing the FFT to simplify the phase relationship of the
97 resulting spectrum. See Amalia de Götzen's paper referred to above.
100 void fvec_shift (fvec_t * v);
102 /** compute the sum of all elements of a vector
104 \param v vector to compute the sum of
109 smpl_t fvec_sum (fvec_t * v);
111 /** compute the High Frequency Content of a vector
113 The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$.
115 \param v vector to get the energy from
120 smpl_t fvec_local_hfc (fvec_t * v);
122 /** computes the p-norm of a vector
124 Computes the p-norm of a vector for \f$ p = \alpha \f$
126 \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$
128 If p = 1, the result is the Manhattan distance.
130 If p = 2, the result is the Euclidean distance.
132 As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the
137 - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on
140 \param v vector to compute norm from
141 \param p order of the computed norm
143 \return the p-norm of v
146 smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p);
148 /** alpha normalisation
150 This function divides all elements of a vector by the p-norm as computed by
153 \param v vector to compute norm from
154 \param p order of the computed norm
157 void fvec_alpha_normalise (fvec_t * v, smpl_t p);
159 /** add a constant to each elements of a vector
161 \param v vector to add constant to
162 \param c constant to add to v
165 void fvec_add (fvec_t * v, smpl_t c);
167 /** remove the minimum value of the vector to each elements
169 \param v vector to remove minimum from
172 void fvec_min_removal (fvec_t * v);
174 /** compute moving median threshold of a vector
176 This function computes the moving median threshold value of at the given
177 position of a vector, taking the median among post elements before and up to
178 pre elements after pos.
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
186 \return moving median threshold value
189 smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
192 /** apply adaptive threshold to a vector
194 For each points at position p of an input vector, this function remove the
195 moving median threshold computed at p.
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
203 void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);
205 /** returns the median of a vector
207 The QuickSelect routine is based on the algorithm described in "Numerical
208 recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
211 This implementation of the QuickSelect routine is based on Nicolas
212 Devillard's implementation, available at http://ndevilla.free.fr/median/median/
213 and in the Public Domain.
215 \param v vector to get median from
217 \return the median of v
220 smpl_t fvec_median (fvec_t * v);
222 /** finds exact peak index by quadratic interpolation
224 See [Quadratic Interpolation of Spectral
225 Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
226 by Julius O. Smith III
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$
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
235 smpl_t fvec_quadratic_peak_pos (fvec_t * x, uint_t p);
237 /** finds magnitude of peak by quadratic interpolation
239 See [Quadratic Interpolation of Spectral
240 Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
241 by Julius O. Smith III
243 \param x vector to get the magnitude of the interpolated peak position from
244 \param p index of the peak in vector `x`
245 \return magnitude of interpolated peak
248 smpl_t fvec_quadratic_peak_mag (fvec_t * x, smpl_t p);
250 /** Quadratic interpolation using Lagrange polynomial.
252 Inspired from ``Comparison of interpolation algorithms in real-time sound
253 processing'', Vladimir Arnost,
255 \param s0,s1,s2 are 3 consecutive samples of a curve
256 \param pf is the floating point index [0;2]
258 \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$
261 smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);
263 /** return 1 if v[p] is a peak and positive, 0 otherwise
265 This function returns 1 if a peak is found at index p in the vector v. The
266 peak is defined as follows:
272 \param v input vector
273 \param p position of supposed for peak
275 \return 1 if a peak is found, 0 otherwise
278 uint_t fvec_peakpick (fvec_t * v, uint_t p);
280 /** return 1 if a is a power of 2, 0 otherwise */
281 uint_t aubio_is_power_of_two(uint_t a);
283 /** return the next power of power of 2 greater than a */
284 uint_t aubio_next_power_of_two(uint_t a);
286 /** compute normalised autocorrelation function
288 \param input vector to compute autocorrelation from
289 \param output vector to store autocorrelation function to
292 void aubio_autocorr (fvec_t * input, fvec_t * output);
298 #endif /* _AUBIO_MATHUTILS_H */