mirror of
https://github.com/mpv-player/mpv
synced 2024-12-14 02:45:43 +00:00
6e9cbdc104
git-svn-id: svn://svn.mplayerhq.hu/mplayer/trunk@29305 b3059339-0415-0410-9bf9-f77b7e298cf2
452 lines
14 KiB
C
452 lines
14 KiB
C
/*
|
|
* design and implementation of different types of digital filters
|
|
*
|
|
* Copyright (C) 2001 Anders Johansson ajh@atri.curtin.edu.au
|
|
*
|
|
* This file is part of MPlayer.
|
|
*
|
|
* MPlayer 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 2 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* MPlayer 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 MPlayer; if not, write to the Free Software Foundation, Inc.,
|
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
|
*/
|
|
|
|
#include <string.h>
|
|
#include <math.h>
|
|
#include "dsp.h"
|
|
|
|
/******************************************************************************
|
|
* FIR filter implementations
|
|
******************************************************************************/
|
|
|
|
/* C implementation of FIR filter y=w*x
|
|
|
|
n number of filter taps, where mod(n,4)==0
|
|
w filter taps
|
|
x input signal must be a circular buffer which is indexed backwards
|
|
*/
|
|
inline FLOAT_TYPE af_filter_fir(register unsigned int n, const FLOAT_TYPE* w,
|
|
const FLOAT_TYPE* x)
|
|
{
|
|
register FLOAT_TYPE y; // Output
|
|
y = 0.0;
|
|
do{
|
|
n--;
|
|
y+=w[n]*x[n];
|
|
}while(n != 0);
|
|
return y;
|
|
}
|
|
|
|
/* C implementation of parallel FIR filter y(k)=w(k) * x(k) (where * denotes convolution)
|
|
|
|
n number of filter taps, where mod(n,4)==0
|
|
d number of filters
|
|
xi current index in xq
|
|
w filter taps k by n big
|
|
x input signal must be a circular buffers which are indexed backwards
|
|
y output buffer
|
|
s output buffer stride
|
|
*/
|
|
FLOAT_TYPE* af_filter_pfir(unsigned int n, unsigned int d, unsigned int xi,
|
|
const FLOAT_TYPE** w, const FLOAT_TYPE** x, FLOAT_TYPE* y,
|
|
unsigned int s)
|
|
{
|
|
register const FLOAT_TYPE* xt = *x + xi;
|
|
register const FLOAT_TYPE* wt = *w;
|
|
register int nt = 2*n;
|
|
while(d-- > 0){
|
|
*y = af_filter_fir(n,wt,xt);
|
|
wt+=n;
|
|
xt+=nt;
|
|
y+=s;
|
|
}
|
|
return y;
|
|
}
|
|
|
|
/* Add new data to circular queue designed to be used with a parallel
|
|
FIR filter, with d filters. xq is the circular queue, in pointing
|
|
at the new samples, xi current index in xq and n the length of the
|
|
filter. xq must be n*2 by k big, s is the index for in.
|
|
*/
|
|
int af_filter_updatepq(unsigned int n, unsigned int d, unsigned int xi,
|
|
FLOAT_TYPE** xq, const FLOAT_TYPE* in, unsigned int s)
|
|
{
|
|
register FLOAT_TYPE* txq = *xq + xi;
|
|
register int nt = n*2;
|
|
|
|
while(d-- >0){
|
|
*txq= *(txq+n) = *in;
|
|
txq+=nt;
|
|
in+=s;
|
|
}
|
|
return (++xi)&(n-1);
|
|
}
|
|
|
|
/******************************************************************************
|
|
* FIR filter design
|
|
******************************************************************************/
|
|
|
|
/* Design FIR filter using the Window method
|
|
|
|
n filter length must be odd for HP and BS filters
|
|
w buffer for the filter taps (must be n long)
|
|
fc cutoff frequencies (1 for LP and HP, 2 for BP and BS)
|
|
0 < fc < 1 where 1 <=> Fs/2
|
|
flags window and filter type as defined in filter.h
|
|
variables are ored together: i.e. LP|HAMMING will give a
|
|
low pass filter designed using a hamming window
|
|
opt beta constant used only when designing using kaiser windows
|
|
|
|
returns 0 if OK, -1 if fail
|
|
*/
|
|
int af_filter_design_fir(unsigned int n, FLOAT_TYPE* w, const FLOAT_TYPE* fc,
|
|
unsigned int flags, FLOAT_TYPE opt)
|
|
{
|
|
unsigned int o = n & 1; // Indicator for odd filter length
|
|
unsigned int end = ((n + 1) >> 1) - o; // Loop end
|
|
unsigned int i; // Loop index
|
|
|
|
FLOAT_TYPE k1 = 2 * M_PI; // 2*pi*fc1
|
|
FLOAT_TYPE k2 = 0.5 * (FLOAT_TYPE)(1 - o);// Constant used if the filter has even length
|
|
FLOAT_TYPE k3; // 2*pi*fc2 Constant used in BP and BS design
|
|
FLOAT_TYPE g = 0.0; // Gain
|
|
FLOAT_TYPE t1,t2,t3; // Temporary variables
|
|
FLOAT_TYPE fc1,fc2; // Cutoff frequencies
|
|
|
|
// Sanity check
|
|
if(!w || (n == 0)) return -1;
|
|
|
|
// Get window coefficients
|
|
switch(flags & WINDOW_MASK){
|
|
case(BOXCAR):
|
|
af_window_boxcar(n,w); break;
|
|
case(TRIANG):
|
|
af_window_triang(n,w); break;
|
|
case(HAMMING):
|
|
af_window_hamming(n,w); break;
|
|
case(HANNING):
|
|
af_window_hanning(n,w); break;
|
|
case(BLACKMAN):
|
|
af_window_blackman(n,w); break;
|
|
case(FLATTOP):
|
|
af_window_flattop(n,w); break;
|
|
case(KAISER):
|
|
af_window_kaiser(n,w,opt); break;
|
|
default:
|
|
return -1;
|
|
}
|
|
|
|
if(flags & (LP | HP)){
|
|
fc1=*fc;
|
|
// Cutoff frequency must be < 0.5 where 0.5 <=> Fs/2
|
|
fc1 = ((fc1 <= 1.0) && (fc1 > 0.0)) ? fc1/2 : 0.25;
|
|
k1 *= fc1;
|
|
|
|
if(flags & LP){ // Low pass filter
|
|
|
|
// If the filter length is odd, there is one point which is exactly
|
|
// in the middle. The value at this point is 2*fCutoff*sin(x)/x,
|
|
// where x is zero. To make sure nothing strange happens, we set this
|
|
// value separately.
|
|
if (o){
|
|
w[end] = fc1 * w[end] * 2.0;
|
|
g=w[end];
|
|
}
|
|
|
|
// Create filter
|
|
for (i=0 ; i<end ; i++){
|
|
t1 = (FLOAT_TYPE)(i+1) - k2;
|
|
w[end-i-1] = w[n-end+i] = w[end-i-1] * sin(k1 * t1)/(M_PI * t1); // Sinc
|
|
g += 2*w[end-i-1]; // Total gain in filter
|
|
}
|
|
}
|
|
else{ // High pass filter
|
|
if (!o) // High pass filters must have odd length
|
|
return -1;
|
|
w[end] = 1.0 - (fc1 * w[end] * 2.0);
|
|
g= w[end];
|
|
|
|
// Create filter
|
|
for (i=0 ; i<end ; i++){
|
|
t1 = (FLOAT_TYPE)(i+1);
|
|
w[end-i-1] = w[n-end+i] = -1 * w[end-i-1] * sin(k1 * t1)/(M_PI * t1); // Sinc
|
|
g += ((i&1) ? (2*w[end-i-1]) : (-2*w[end-i-1])); // Total gain in filter
|
|
}
|
|
}
|
|
}
|
|
|
|
if(flags & (BP | BS)){
|
|
fc1=fc[0];
|
|
fc2=fc[1];
|
|
// Cutoff frequencies must be < 1.0 where 1.0 <=> Fs/2
|
|
fc1 = ((fc1 <= 1.0) && (fc1 > 0.0)) ? fc1/2 : 0.25;
|
|
fc2 = ((fc2 <= 1.0) && (fc2 > 0.0)) ? fc2/2 : 0.25;
|
|
k3 = k1 * fc2; // 2*pi*fc2
|
|
k1 *= fc1; // 2*pi*fc1
|
|
|
|
if(flags & BP){ // Band pass
|
|
// Calculate center tap
|
|
if (o){
|
|
g=w[end]*(fc1+fc2);
|
|
w[end] = (fc2 - fc1) * w[end] * 2.0;
|
|
}
|
|
|
|
// Create filter
|
|
for (i=0 ; i<end ; i++){
|
|
t1 = (FLOAT_TYPE)(i+1) - k2;
|
|
t2 = sin(k3 * t1)/(M_PI * t1); // Sinc fc2
|
|
t3 = sin(k1 * t1)/(M_PI * t1); // Sinc fc1
|
|
g += w[end-i-1] * (t3 + t2); // Total gain in filter
|
|
w[end-i-1] = w[n-end+i] = w[end-i-1] * (t2 - t3);
|
|
}
|
|
}
|
|
else{ // Band stop
|
|
if (!o) // Band stop filters must have odd length
|
|
return -1;
|
|
w[end] = 1.0 - (fc2 - fc1) * w[end] * 2.0;
|
|
g= w[end];
|
|
|
|
// Create filter
|
|
for (i=0 ; i<end ; i++){
|
|
t1 = (FLOAT_TYPE)(i+1);
|
|
t2 = sin(k1 * t1)/(M_PI * t1); // Sinc fc1
|
|
t3 = sin(k3 * t1)/(M_PI * t1); // Sinc fc2
|
|
w[end-i-1] = w[n-end+i] = w[end-i-1] * (t2 - t3);
|
|
g += 2*w[end-i-1]; // Total gain in filter
|
|
}
|
|
}
|
|
}
|
|
|
|
// Normalize gain
|
|
g=1/g;
|
|
for (i=0; i<n; i++)
|
|
w[i] *= g;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Design polyphase FIR filter from prototype filter
|
|
|
|
n length of prototype filter
|
|
k number of polyphase components
|
|
w prototype filter taps
|
|
pw Parallel FIR filter
|
|
g Filter gain
|
|
flags FWD forward indexing
|
|
REW reverse indexing
|
|
ODD multiply every 2nd filter tap by -1 => HP filter
|
|
|
|
returns 0 if OK, -1 if fail
|
|
*/
|
|
int af_filter_design_pfir(unsigned int n, unsigned int k, const FLOAT_TYPE* w,
|
|
FLOAT_TYPE** pw, FLOAT_TYPE g, unsigned int flags)
|
|
{
|
|
int l = (int)n/k; // Length of individual FIR filters
|
|
int i; // Counters
|
|
int j;
|
|
FLOAT_TYPE t; // g * w[i]
|
|
|
|
// Sanity check
|
|
if(l<1 || k<1 || !w || !pw)
|
|
return -1;
|
|
|
|
// Do the stuff
|
|
if(flags&REW){
|
|
for(j=l-1;j>-1;j--){//Columns
|
|
for(i=0;i<(int)k;i++){//Rows
|
|
t=g * *w++;
|
|
pw[i][j]=t * ((flags & ODD) ? ((j & 1) ? -1 : 1) : 1);
|
|
}
|
|
}
|
|
}
|
|
else{
|
|
for(j=0;j<l;j++){//Columns
|
|
for(i=0;i<(int)k;i++){//Rows
|
|
t=g * *w++;
|
|
pw[i][j]=t * ((flags & ODD) ? ((j & 1) ? 1 : -1) : 1);
|
|
}
|
|
}
|
|
}
|
|
return -1;
|
|
}
|
|
|
|
/******************************************************************************
|
|
* IIR filter design
|
|
******************************************************************************/
|
|
|
|
/* Helper functions for the bilinear transform */
|
|
|
|
/* Pre-warp the coefficients of a numerator or denominator.
|
|
Note that a0 is assumed to be 1, so there is no wrapping
|
|
of it.
|
|
*/
|
|
static void af_filter_prewarp(FLOAT_TYPE* a, FLOAT_TYPE fc, FLOAT_TYPE fs)
|
|
{
|
|
FLOAT_TYPE wp;
|
|
wp = 2.0 * fs * tan(M_PI * fc / fs);
|
|
a[2] = a[2]/(wp * wp);
|
|
a[1] = a[1]/wp;
|
|
}
|
|
|
|
/* Transform the numerator and denominator coefficients of s-domain
|
|
biquad section into corresponding z-domain coefficients.
|
|
|
|
The transfer function for z-domain is:
|
|
|
|
1 + alpha1 * z^(-1) + alpha2 * z^(-2)
|
|
H(z) = -------------------------------------
|
|
1 + beta1 * z^(-1) + beta2 * z^(-2)
|
|
|
|
Store the 4 IIR coefficients in array pointed by coef in following
|
|
order:
|
|
beta1, beta2 (denominator)
|
|
alpha1, alpha2 (numerator)
|
|
|
|
Arguments:
|
|
a - s-domain numerator coefficients
|
|
b - s-domain denominator coefficients
|
|
k - filter gain factor. Initially set to 1 and modified by each
|
|
biquad section in such a way, as to make it the
|
|
coefficient by which to multiply the overall filter gain
|
|
in order to achieve a desired overall filter gain,
|
|
specified in initial value of k.
|
|
fs - sampling rate (Hz)
|
|
coef - array of z-domain coefficients to be filled in.
|
|
|
|
Return: On return, set coef z-domain coefficients and k to the gain
|
|
required to maintain overall gain = 1.0;
|
|
*/
|
|
static void af_filter_bilinear(const FLOAT_TYPE* a, const FLOAT_TYPE* b, FLOAT_TYPE* k,
|
|
FLOAT_TYPE fs, FLOAT_TYPE *coef)
|
|
{
|
|
FLOAT_TYPE ad, bd;
|
|
|
|
/* alpha (Numerator in s-domain) */
|
|
ad = 4. * a[2] * fs * fs + 2. * a[1] * fs + a[0];
|
|
/* beta (Denominator in s-domain) */
|
|
bd = 4. * b[2] * fs * fs + 2. * b[1] * fs + b[0];
|
|
|
|
/* Update gain constant for this section */
|
|
*k *= ad/bd;
|
|
|
|
/* Denominator */
|
|
*coef++ = (2. * b[0] - 8. * b[2] * fs * fs)/bd; /* beta1 */
|
|
*coef++ = (4. * b[2] * fs * fs - 2. * b[1] * fs + b[0])/bd; /* beta2 */
|
|
|
|
/* Numerator */
|
|
*coef++ = (2. * a[0] - 8. * a[2] * fs * fs)/ad; /* alpha1 */
|
|
*coef = (4. * a[2] * fs * fs - 2. * a[1] * fs + a[0])/ad; /* alpha2 */
|
|
}
|
|
|
|
|
|
|
|
/* IIR filter design using bilinear transform and prewarp. Transforms
|
|
2nd order s domain analog filter into a digital IIR biquad link. To
|
|
create a filter fill in a, b, Q and fs and make space for coef and k.
|
|
|
|
|
|
Example Butterworth design:
|
|
|
|
Below are Butterworth polynomials, arranged as a series of 2nd
|
|
order sections:
|
|
|
|
Note: n is filter order.
|
|
|
|
n Polynomials
|
|
-------------------------------------------------------------------
|
|
2 s^2 + 1.4142s + 1
|
|
4 (s^2 + 0.765367s + 1) * (s^2 + 1.847759s + 1)
|
|
6 (s^2 + 0.5176387s + 1) * (s^2 + 1.414214 + 1) * (s^2 + 1.931852s + 1)
|
|
|
|
For n=4 we have following equation for the filter transfer function:
|
|
1 1
|
|
T(s) = --------------------------- * ----------------------------
|
|
s^2 + (1/Q) * 0.765367s + 1 s^2 + (1/Q) * 1.847759s + 1
|
|
|
|
The filter consists of two 2nd order sections since highest s power
|
|
is 2. Now we can take the coefficients, or the numbers by which s
|
|
is multiplied and plug them into a standard formula to be used by
|
|
bilinear transform.
|
|
|
|
Our standard form for each 2nd order section is:
|
|
|
|
a2 * s^2 + a1 * s + a0
|
|
H(s) = ----------------------
|
|
b2 * s^2 + b1 * s + b0
|
|
|
|
Note that Butterworth numerator is 1 for all filter sections, which
|
|
means s^2 = 0 and s^1 = 0
|
|
|
|
Let's convert standard Butterworth polynomials into this form:
|
|
|
|
0 + 0 + 1 0 + 0 + 1
|
|
--------------------------- * --------------------------
|
|
1 + ((1/Q) * 0.765367) + 1 1 + ((1/Q) * 1.847759) + 1
|
|
|
|
Section 1:
|
|
a2 = 0; a1 = 0; a0 = 1;
|
|
b2 = 1; b1 = 0.765367; b0 = 1;
|
|
|
|
Section 2:
|
|
a2 = 0; a1 = 0; a0 = 1;
|
|
b2 = 1; b1 = 1.847759; b0 = 1;
|
|
|
|
Q is filter quality factor or resonance, in the range of 1 to
|
|
1000. The overall filter Q is a product of all 2nd order stages.
|
|
For example, the 6th order filter (3 stages, or biquads) with
|
|
individual Q of 2 will have filter Q = 2 * 2 * 2 = 8.
|
|
|
|
|
|
Arguments:
|
|
a - s-domain numerator coefficients, a[1] is always assumed to be 1.0
|
|
b - s-domain denominator coefficients
|
|
Q - Q value for the filter
|
|
k - filter gain factor. Initially set to 1 and modified by each
|
|
biquad section in such a way, as to make it the
|
|
coefficient by which to multiply the overall filter gain
|
|
in order to achieve a desired overall filter gain,
|
|
specified in initial value of k.
|
|
fs - sampling rate (Hz)
|
|
coef - array of z-domain coefficients to be filled in.
|
|
|
|
Note: Upon return from each call, the k argument will be set to a
|
|
value, by which to multiply our actual signal in order for the gain
|
|
to be one. On second call to szxform() we provide k that was
|
|
changed by the previous section. During actual audio filtering
|
|
k can be used for gain compensation.
|
|
|
|
return -1 if fail 0 if success.
|
|
*/
|
|
int af_filter_szxform(const FLOAT_TYPE* a, const FLOAT_TYPE* b, FLOAT_TYPE Q, FLOAT_TYPE fc,
|
|
FLOAT_TYPE fs, FLOAT_TYPE *k, FLOAT_TYPE *coef)
|
|
{
|
|
FLOAT_TYPE at[3];
|
|
FLOAT_TYPE bt[3];
|
|
|
|
if(!a || !b || !k || !coef || (Q>1000.0 || Q< 1.0))
|
|
return -1;
|
|
|
|
memcpy(at,a,3*sizeof(FLOAT_TYPE));
|
|
memcpy(bt,b,3*sizeof(FLOAT_TYPE));
|
|
|
|
bt[1]/=Q;
|
|
|
|
/* Calculate a and b and overwrite the original values */
|
|
af_filter_prewarp(at, fc, fs);
|
|
af_filter_prewarp(bt, fc, fs);
|
|
/* Execute bilinear transform */
|
|
af_filter_bilinear(at, bt, k, fs, coef);
|
|
|
|
return 0;
|
|
}
|
|
|