Filtering utility functions. More...

Detailed Description

Filtering utility functions.

Author: Pascal Getreuer getre.nosp@m.uer@.nosp@m.cmla..nosp@m.ens-.nosp@m.cacha.nosp@m.n.fr

This program is free software: you can redistribute it and/or modify it under, at your option, 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, or the terms of the simplified BSD license.

You should have received a copy of these licenses along with this program. If not, see http://www.gnu.org/licenses/ and http://www.opensource.org/licenses/bsd-license.html.

Definition in file filter_util.c.

#include "filter_util.h"
#include <assert.h>
#include <math.h>
#include <string.h>

Go to the source code of this file.

Macros
#define	MAX_Q 7
	Maximum possible value of q in init_recursive_filter()

Functions
void	recursive_filter_impulse (num h, long N, const num b, int p, const num *a, int q)
	Compute taps of the impulse response of a causal recursive filter. More...

void	init_recursive_filter (num dest, const num src, long N, long stride, const num b, int p, const num a, int q, num sum, num tol, long max_iter)
	Initialize a causal recursive filter with boundary extension. More...

Function Documentation

void init_recursive_filter	(	num *	dest,
		const num *	src,
		long	N,
		long	stride,
		const num *	b,
		int	p,
		const num *	a,
		int	q,
		num	sum,
		num	tol,
		long	max_iter
	)

Initialize a causal recursive filter with boundary extension.

Parameters

dest	destination array with size of at least q
src	input signal of length N
N	length of src
stride	the stride between successive samples of src
b	numerator coefficients
p	largest delay of the numerator
a	denominator coefficients
q	largest delay of the denominator
sum	the L^1 norm of the impulse response
tol	accuracy tolerance
max_iter	maximum number of samples to use for approximation

This routine initializes a recursive filter,

$\begin{aligned} u_n &= b_0 f_n + b_1 f_{n-1} + \cdots + b_p f_{n-p} &\quad - a_1 u_{n-1} - a_2 u_{n-2} - \cdots - a_q u_{n-q}, \end{aligned}$

with boundary extension by approximating the infinite sum

$u_m=\sum_{n=-m}^\infty h_{n+m}\Tilde{f}_{-n} \approx \sum_{n=-m}^{k-1} h_{n+m} \Tilde{f}_{-n}, \quad m = 0, \ldots, q - 1.$

Definition at line 86 of file filter_util.c.

void recursive_filter_impulse	(	num *	h,
		long	N,
		const num *	b,
		int	p,
		const num *	a,
		int	q
	)

Compute taps of the impulse response of a causal recursive filter.

Parameters

h	destination array of size N
N	number of taps to compute (beginning from n = 0)
b	numerator coefficients
p	largest delay of the numerator
a	denominator coefficients
q	largest delay of the denominator

Computes taps $h_0, \ldots, h_{N-1}$ of the impulse response of the recursive filter

$H(z) = \frac{b[0] + b[1]z^{-1} + \cdots + b[p]z^{-p}} {1 + a[1]z^{-1} + \cdots + a[q]z^{-q}},$

or equivalently

$\begin{aligned} h[n] = & b[0]\delta_n + b[1]\delta_{n-1}+\cdots + b[p]\delta_{n-p}\\ & -a[1]h[n-1]-\cdots -a[q]h[n-q], \end{aligned}$

for n = 0, ..., N-1 where $\delta$ is the unit impulse. In the denominator coefficient array, element a[0] is not used.

Definition at line 47 of file filter_util.c.

Detailed Description

Macros

Functions

Function Documentation