Various math functions. More...

#include "fvec.h"
#include "musicutils.h"

Functions
smpl_t	fvec_mean (fvec_t *s)
	compute the mean of a vector More...

smpl_t	fvec_max (fvec_t *s)
	find the max of a vector More...

smpl_t	fvec_min (fvec_t *s)
	find the min of a vector More...

uint_t	fvec_min_elem (fvec_t *s)
	find the index of the min of a vector More...

uint_t	fvec_max_elem (fvec_t *s)
	find the index of the max of a vector More...

void	fvec_shift (fvec_t *v)
	swap the left and right halves of a vector More...

smpl_t	fvec_sum (fvec_t *v)
	compute the sum of all elements of a vector More...

smpl_t	fvec_local_hfc (fvec_t *v)
	compute the High Frequency Content of a vector More...

smpl_t	fvec_alpha_norm (fvec_t *v, smpl_t p)
	computes the p-norm of a vector More...

void	fvec_alpha_normalise (fvec_t *v, smpl_t p)
	alpha normalisation More...

void	fvec_add (fvec_t *v, smpl_t c)
	add a constant to each elements of a vector More...

void	fvec_min_removal (fvec_t *v)
	remove the minimum value of the vector to each elements More...

smpl_t	fvec_moving_thres (fvec_t v, fvec_t tmp, uint_t post, uint_t pre, uint_t pos)
	compute moving median threshold of a vector More...

void	fvec_adapt_thres (fvec_t v, fvec_t tmp, uint_t post, uint_t pre)
	apply adaptive threshold to a vector More...

smpl_t	fvec_median (fvec_t *v)
	returns the median of a vector More...

smpl_t	fvec_quadratic_peak_pos (fvec_t *x, uint_t p)
	finds exact peak index by quadratic interpolation More...

smpl_t	aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf)
	Quadratic interpolation using Lagrange polynomial. More...

uint_t	fvec_peakpick (fvec_t *v, uint_t p)
	return 1 if v[p] is a peak and positive, 0 otherwise More...

uint_t	aubio_is_power_of_two (uint_t a)
	return 1 if a is a power of 2, 0 otherwise

uint_t	aubio_next_power_of_two (uint_t a)
	return the next power of power of 2 greater than a

void	aubio_autocorr (fvec_t input, fvec_t output)
	compute normalised autocorrelation function More...

Detailed Description

Various math functions.

Definition in file mathutils.h.

Function Documentation

void aubio_autocorr	(	fvec_t *	input,
		fvec_t *	output
	)

compute normalised autocorrelation function

Parameters

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

smpl_t aubio_quadfrac	(	smpl_t	s0,
		smpl_t	s1,
		smpl_t	s2,
		smpl_t	pf
	)

Quadratic interpolation using Lagrange polynomial.

Inspired from ``Comparison of interpolation algorithms in real-time sound processing'', Vladimir Arnost,

Parameters

s0,s1,s2	are 3 consecutive samples of a curve
pf	is the floating point index [0;2]

Returns: \( s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \)

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

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.

Parameters

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

void fvec_add	(	fvec_t *	v,
		smpl_t	c
	)

add a constant to each elements of a vector

Parameters

v	vector to add constant to
c	constant to add to v

smpl_t fvec_alpha_norm	(	fvec_t *	v,
		smpl_t	p
	)

computes the p-norm of a vector

Computes the p-norm of a vector for \( p = \alpha \)

\( L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \)

If p = 1, the result is the Manhattan distance.

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

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

References:

\(L^p\) space on Wikipedia

Parameters

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

Returns: the p-norm of v

void fvec_alpha_normalise	(	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().

Parameters

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

smpl_t fvec_local_hfc ( fvec_t * v )

compute the High Frequency Content of a vector

The High Frequency Content is defined as \( \sum_0^{N-1} (k+1) v[k] \).

Parameters

v	vector to get the energy from

Returns: the HFC of v

smpl_t fvec_max ( fvec_t * s )

find the max of a vector

Parameters

s	vector to get the max from

Returns: the value of the minimum of v

uint_t fvec_max_elem ( fvec_t * s )

find the index of the max of a vector

Parameters

s	vector to get the index from

Returns: the index of the maximum element of v

smpl_t fvec_mean ( fvec_t * s )

compute the mean of a vector

Parameters

s	vector to compute mean from

Returns: the mean of v

smpl_t fvec_median ( fvec_t * v )

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.

Parameters

v	vector to get median from

Returns: the median of v

Examples:: examples/aubionotes.c.

smpl_t fvec_min ( fvec_t * s )

find the min of a vector

Parameters

s	vector to get the min from

Returns: the value of the maximum of v

uint_t fvec_min_elem ( fvec_t * s )

find the index of the min of a vector

Parameters

s	vector to get the index from

Returns: the index of the minimum element of v

void fvec_min_removal ( fvec_t * v )

remove the minimum value of the vector to each elements

Parameters

v	vector to remove minimum from

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

compute moving median threshold of a vector

This function computes the moving median threshold value of at the given position of a vector, taking the median among post elements before and up to pre elements after pos.

Parameters

v	input vector
tmp	temporary vector of length post+1+pre
post	length of causal part to take before pos
pre	length of anti-causal part to take after pos
pos	index to compute threshold for

Returns: moving median threshold value

uint_t fvec_peakpick	(	fvec_t *	v,
		uint_t	p
	)

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]

Parameters

v	input vector
p	position of supposed for peak

Returns: 1 if a peak is found, 0 otherwise

smpl_t fvec_quadratic_peak_pos	(	fvec_t *	x,
		uint_t	p
	)

finds exact peak index by quadratic interpolation

See Quadratic Interpolation of Spectral Peaks, by Julius O. Smith III

\( p_{frac} = \frac{1}{2} \frac {x[p-1] - x[p+1]} {x[p-1] - 2 x[p] + x[p+1]} \in [ -.5, .5] \)

Parameters

x	vector to get the interpolated peak position from
p	index of the peak in vector `x`

Returns: \( p + p_{frac} \) exact peak position of interpolated maximum or minimum

void fvec_shift ( fvec_t * v )

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

\( a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \)

becomes

\( a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \)

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.

smpl_t fvec_sum ( fvec_t * v )

compute the sum of all elements of a vector

Parameters

v	vector to compute the sum of

Returns: the sum of v

Functions

Detailed Description

Function Documentation