source: src/mathutils.h @ eb089fb

/*
  Copyright (C) 2003-2009 Paul Brossier <piem@aubio.org>

  This file is part of aubio.

  aubio is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.

  aubio is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with aubio.  If not, see <http://www.gnu.org/licenses/>.

*/

/** @file
 *  various math functions
 */

#ifndef MATHUTILS_H
#define MATHUTILS_H

#ifdef __cplusplus
extern "C" {
#endif

/** Window types 
 
  References:
    
    - <a href="http://en.wikipedia.org/wiki/Window_function">Window
function</a> on Wikipedia
    - Amalia de Götzen, Nicolas Bernardini, and Daniel Arfib. Traditional (?)
implementations of a phase vocoder: the tricks of the trade. In Proceedings of
the International Conference on Digital Audio Effects (DAFx-00), pages 37–44,
Uni- versity of Verona, Italy, 2000.
  (<a href="http://profs.sci.univr.it/%7Edafx/Final-Papers/ps/Bernardini.ps.gz">
  ps.gz</a>)

*/
typedef enum
{
  aubio_win_rectangle,
  aubio_win_hamming,
  aubio_win_hanning,
  aubio_win_hanningz,
  aubio_win_blackman,
  aubio_win_blackman_harris,
  aubio_win_gaussian,
  aubio_win_welch,
  aubio_win_parzen
} aubio_window_type;

/** create window */
fvec_t *new_aubio_window (uint_t size, aubio_window_type wintype);

/** compute the principal argument

  This function maps the input phase to its corresponding value wrapped in the
range \f$ [-\pi, \pi] \f$.

  \param phase unwrapped phase to map to the unit circle
  
  \return equivalent phase wrapped to the unit circle

*/
smpl_t aubio_unwrap2pi (smpl_t phase);

/** compute the mean of a vector

  \param s vector to compute norm from

  \return the mean of v

*/
smpl_t fvec_mean (fvec_t * s);

/** find the max of a vector

  \param s vector to get the max from

  \return the value of the minimum of v

*/
smpl_t fvec_max (fvec_t * s);

/** find the min of a vector

  \param s vector to get the min from

  \return the value of the maximum of v

*/
smpl_t fvec_min (fvec_t * s);

/** find the index of the min of a vector

  \param s vector to get the index from

  \return the index of the minimum element of v

*/
uint_t fvec_min_elem (fvec_t * s);

/** find the index of the max of a vector

  \param s vector to get the index from

  \return the index of the maximum element of v

*/
uint_t fvec_max_elem (fvec_t * s);

/** swap the left and right halves of a vector
  
  This function swaps the left part of the signal with the right part of the
signal. Therefore

  \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$
  
  becomes
  
  \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$

  This operation, known as 'fftshift' in the Matlab Signal Processing Toolbox,
can be used before computing the FFT to simplify the phase relationship of the
resulting spectrum. See Amalia de Götzen's paper referred to above.
  
*/
void fvec_shift (fvec_t * v);

/** compute the sum of all elements of a vector

  \param v vector to compute the sum of

  \return the sum of v

*/
smpl_t fvec_sum (fvec_t * v);

/** compute the energy of a vector

  This function compute the sum of the squared elements of a vector.
 
  \param v vector to get the energy from 

  \return the energy of v
 
*/
smpl_t fvec_local_energy (fvec_t * v);

/** compute the High Frequency Content of a vector

  The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$.
 
  \param v vector to get the energy from 

  \return the HFC of v
 
*/
smpl_t fvec_local_hfc (fvec_t * v);

/** computes the p-norm of a vector 
 
  Computes the p-norm of a vector for \f$ p = \alpha \f$

  \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$
  
  If p = 1, the result is the Manhattan distance.

  If p = 2, the result is the Euclidean distance.

  As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the
input vector.

  References:
  
    - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on
  Wikipedia

  \param v vector to compute norm from
  \param p order of the computed norm

  \return the p-norm of v
 
*/
smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p);

/**  alpha normalisation

  This function divides all elements of a vector by the p-norm as computed by 
fvec_alpha_norm().

  \param v vector to compute norm from
  \param p order of the computed norm

*/
void fvec_alpha_normalise (fvec_t * v, smpl_t p);

/** add a constant to each elements of a vector

  \param v vector to add constant to
  \param c constant to add to v

*/
void fvec_add (fvec_t * v, smpl_t c);

/** remove the minimum value of the vector to each elements
  
  \param v vector to remove minimum from

*/
void fvec_min_removal (fvec_t * v);

/** compute moving median theshold of a vector

  This function computes the moving median threshold value of at the given
position of a vector, taking the median amongs post elements before and up to
pre elements after pos.
 
  \param v input vector
  \param tmp temporary vector of length post+1+pre
  \param post length of causal part to take before pos 
  \param pre length of anti-causal part to take after pos
  \param pos index to compute threshold for 

  \return moving median threshold value 

*/
smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
    uint_t pos);

/** apply adaptive threshold to a vector

  For each points at position p of an input vector, this function remove the
moving median threshold computed at p.

  \param v input vector
  \param tmp temporary vector of length post+1+pre
  \param post length of causal part to take before pos 
  \param pre length of anti-causal part to take after pos

*/
void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);

/** returns the median of a vector 

  The QuickSelect routine is based on the algorithm described in "Numerical
recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
ISBN 0-521-43108-5

  This implementation of the QuickSelect routine is based on Nicolas
Devillard's implementation, available at http://ndevilla.free.fr/median/median/
and in the Public Domain.

  \param v vector to get median from

  \return the median of v
 
*/
smpl_t fvec_median (fvec_t * v);

/** finds exact peak index by quadratic interpolation*/
smpl_t fvec_quadint (fvec_t * x, uint_t pos, uint_t span);

/** Quadratic interpolation using Lagrange polynomial.
 
  Inspired from ``Comparison of interpolation algorithms in real-time sound
processing'', Vladimir Arnost, 
  
  \param s0,s1,s2 are 3 consecutive samples of a curve 
  \param pf is the floating point index [0;2]
 
  \return s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2);

*/
smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);

/** return 1 if v[p] is a peak and positive, 0 otherwise

  This function returns 1 if a peak is found at index p in the vector v. The
peak is defined as follows:

  - v[p] is positive
  - v[p-1] < v[p]
  - v[p] > v[p+1]

  \param v input vector
  \param p position of supposed for peak

  \return 1 if a peak is found, 0 otherwise

*/
uint_t fvec_peakpick (fvec_t * v, uint_t p);

/** convert frequency bin to midi value */
smpl_t aubio_bintomidi (smpl_t bin, smpl_t samplerate, smpl_t fftsize);

/** convert midi value to frequency bin */
smpl_t aubio_miditobin (smpl_t midi, smpl_t samplerate, smpl_t fftsize);

/** convert frequency bin to frequency (Hz) */
smpl_t aubio_bintofreq (smpl_t bin, smpl_t samplerate, smpl_t fftsize);

/** convert frequency (Hz) to frequency bin */
smpl_t aubio_freqtobin (smpl_t freq, smpl_t samplerate, smpl_t fftsize);

/** convert frequency (Hz) to midi value (0-128) */
smpl_t aubio_freqtomidi (smpl_t freq);

/** convert midi value (0-128) to frequency (Hz) */
smpl_t aubio_miditofreq (smpl_t midi);

/** compute sound pressure level (SPL) in dB

  This quantity is often wrongly called 'loudness'.

  \param v vector to compute dB SPL from

  \return level of v in dB SPL

*/
smpl_t aubio_db_spl (fvec_t * v);

/** check if buffer level in dB SPL is under a given threshold
 
  \param v vector to get level from
  \param threshold threshold in dB SPL

  \return 0 if level is under the given threshold, 1 otherwise

*/
uint_t aubio_silence_detection (fvec_t * v, smpl_t threshold);

/** get buffer level if level >= threshold, 1. otherwise

  \param v vector to get level from
  \param threshold threshold in dB SPL

  \return level in dB SPL if level >= threshold, 1. otherwise

*/
smpl_t aubio_level_detection (fvec_t * v, smpl_t threshold);

/** compute normalised autocorrelation function

  \param input vector to compute autocorrelation from
  \param output vector to store autocorrelation function to

*/
void aubio_autocorr (fvec_t * input, fvec_t * output);

/** zero-crossing rate (ZCR)

  The zero-crossing rate is the number of times a signal changes sign,
  divided by the length of this signal.

  \param v vector to compute ZCR from

  \return zero-crossing rate of v

*/
smpl_t aubio_zero_crossing_rate (fvec_t * v);

/** clean up cached memory at the end of program
 
  This function should be used at the end of programs to purge all cached
  memory. So far it is only useful to clean FFTW's cache.

*/
void aubio_cleanup (void);

#ifdef __cplusplus
}
#endif

#endif