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mpv/libaf/filter.c

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/*=============================================================================
//
// This software has been released under the terms of the GNU General Public
// license. See http://www.gnu.org/copyleft/gpl.html for details.
//
// Copyright 2001 Anders Johansson ajh@atri.curtin.edu.au
//
//=============================================================================
*/
/* Design and implementation of different types of digital filters
*/
#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 _ftype_t fir(register unsigned int n, _ftype_t* w, _ftype_t* x)
{
register _ftype_t 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
*/
inline _ftype_t* pfir(unsigned int n, unsigned int d, unsigned int xi, _ftype_t** w, _ftype_t** x, _ftype_t* y, unsigned int s)
{
register _ftype_t* xt = *x + xi;
register _ftype_t* wt = *w;
register int nt = 2*n;
while(d-- > 0){
*y = 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.
*/
inline int updatepq(unsigned int n, unsigned int d, unsigned int xi, _ftype_t** xq, _ftype_t* in, unsigned int s)
{
register _ftype_t* 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 design_fir(unsigned int n, _ftype_t* w, _ftype_t* fc, unsigned int flags, _ftype_t 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
_ftype_t k1 = 2 * M_PI; // 2*pi*fc1
_ftype_t k2 = 0.5 * (_ftype_t)(1 - o);// Constant used if the filter has even length
_ftype_t k3; // 2*pi*fc2 Constant used in BP and BS design
_ftype_t g = 0.0; // Gain
_ftype_t t1,t2,t3; // Temporary variables
_ftype_t fc1,fc2; // Cutoff frequencies
// Sanity check
if(!w || (n == 0)) return -1;
// Get window coefficients
switch(flags & WINDOW_MASK){
case(BOXCAR):
boxcar(n,w); break;
case(TRIANG):
triang(n,w); break;
case(HAMMING):
hamming(n,w); break;
case(HANNING):
hanning(n,w); break;
case(BLACKMAN):
blackman(n,w); break;
case(FLATTOP):
flattop(n,w); break;
case(KAISER):
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 = (_ftype_t)(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 = (_ftype_t)(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 = (_ftype_t)(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 = (_ftype_t)(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 design_pfir(unsigned int n, unsigned int k, _ftype_t* w, _ftype_t** pw, _ftype_t g, unsigned int flags)
{
int l = (int)n/k; // Length of individual FIR filters
int i; // Counters
int j;
_ftype_t 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.
*/
void prewarp(_ftype_t* a, _ftype_t fc, _ftype_t fs)
{
_ftype_t 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;
*/
void bilinear(_ftype_t* a, _ftype_t* b, _ftype_t* k, _ftype_t fs, _ftype_t *coef)
{
_ftype_t 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 szxform(_ftype_t* a, _ftype_t* b, _ftype_t Q, _ftype_t fc, _ftype_t fs, _ftype_t *k, _ftype_t *coef)
{
_ftype_t at[3];
_ftype_t bt[3];
if(!a || !b || !k || !coef || (Q>1000.0 || Q< 1.0))
return -1;
memcpy(at,a,3*sizeof(_ftype_t));
memcpy(bt,b,3*sizeof(_ftype_t));
bt[1]/=Q;
/* Calculate a and b and overwrite the original values */
prewarp(at, fc, fs);
prewarp(bt, fc, fs);
/* Execute bilinear transform */
bilinear(at, bt, k, fs, coef);
return 0;
}
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