2 Copyright (C) 2003-2015 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 /** swap the left and right halves of a vector
104 This function swaps the left part of the signal with the right part of the
107 \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$
111 \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$
113 This operation, known as 'ifftshift' in the Matlab Signal Processing Toolbox,
114 can be used after computing the inverse FFT to simplify the phase relationship
115 of the resulting spectrum. See Amalia de Götzen's paper referred to above.
118 void fvec_ishift (fvec_t * v);
120 /** compute the sum of all elements of a vector
122 \param v vector to compute the sum of
127 smpl_t fvec_sum (fvec_t * v);
129 /** compute the High Frequency Content of a vector
131 The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$.
133 \param v vector to get the energy from
138 smpl_t fvec_local_hfc (fvec_t * v);
140 /** computes the p-norm of a vector
142 Computes the p-norm of a vector for \f$ p = \alpha \f$
144 \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$
146 If p = 1, the result is the Manhattan distance.
148 If p = 2, the result is the Euclidean distance.
150 As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the
155 - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on
158 \param v vector to compute norm from
159 \param p order of the computed norm
161 \return the p-norm of v
164 smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p);
166 /** alpha normalisation
168 This function divides all elements of a vector by the p-norm as computed by
171 \param v vector to compute norm from
172 \param p order of the computed norm
175 void fvec_alpha_normalise (fvec_t * v, smpl_t p);
177 /** add a constant to each elements of a vector
179 \param v vector to add constant to
180 \param c constant to add to v
183 void fvec_add (fvec_t * v, smpl_t c);
185 /** remove the minimum value of the vector to each elements
187 \param v vector to remove minimum from
190 void fvec_min_removal (fvec_t * v);
192 /** compute moving median threshold of a vector
194 This function computes the moving median threshold value of at the given
195 position of a vector, taking the median among post elements before and up to
196 pre elements after pos.
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
204 \return moving median threshold value
207 smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
210 /** apply adaptive threshold to a vector
212 For each points at position p of an input vector, this function remove the
213 moving median threshold computed at p.
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
221 void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);
223 /** returns the median of a vector
225 The QuickSelect routine is based on the algorithm described in "Numerical
226 recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
229 This implementation of the QuickSelect routine is based on Nicolas
230 Devillard's implementation, available at http://ndevilla.free.fr/median/median/
231 and in the Public Domain.
233 \param v vector to get median from
235 \return the median of v
238 smpl_t fvec_median (fvec_t * v);
240 /** finds exact peak index by quadratic interpolation
242 See [Quadratic Interpolation of Spectral
243 Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
244 by Julius O. Smith III
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$
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
253 smpl_t fvec_quadratic_peak_pos (const fvec_t * x, uint_t p);
255 /** finds magnitude of peak by quadratic interpolation
257 See [Quadratic Interpolation of Spectral
258 Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
259 by Julius O. Smith III
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
266 smpl_t fvec_quadratic_peak_mag (fvec_t * x, smpl_t p);
268 /** Quadratic interpolation using Lagrange polynomial.
270 Inspired from ``Comparison of interpolation algorithms in real-time sound
271 processing'', Vladimir Arnost,
273 \param s0,s1,s2 are 3 consecutive samples of a curve
274 \param pf is the floating point index [0;2]
276 \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$
279 smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);
281 /** return 1 if v[p] is a peak and positive, 0 otherwise
283 This function returns 1 if a peak is found at index p in the vector v. The
284 peak is defined as follows:
290 \param v input vector
291 \param p position of supposed for peak
293 \return 1 if a peak is found, 0 otherwise
296 uint_t fvec_peakpick (const fvec_t * v, uint_t p);
298 /** return 1 if a is a power of 2, 0 otherwise */
299 uint_t aubio_is_power_of_two(uint_t a);
301 /** return the next power of power of 2 greater than a */
302 uint_t aubio_next_power_of_two(uint_t a);
304 /** compute normalised autocorrelation function
306 \param input vector to compute autocorrelation from
307 \param output vector to store autocorrelation function to
310 void aubio_autocorr (const fvec_t * input, fvec_t * output);
316 #endif /* AUBIO_MATHUTILS_H */