Resonant Lowpass Filter Soruce
// ----------------- file filterIIR00.c begin -----------------
/*
Resonant low pass filter source code.
By baltrax@hotmail.com (Zxform)
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
/**************************************************************************
FILTER.C - Source code for filter functions
iir_filter IIR filter floats sample by sample (real time)
*************************************************************************/
/* FILTER INFORMATION STRUCTURE FOR FILTER ROUTINES */
typedef struct {
unsigned int length; /* size of filter */
float *history; /* pointer to history in filter */
float *coef; /* pointer to coefficients of filter */
} FILTER;
#define FILTER_SECTIONS 2 /* 2 filter sections for 24 db/oct filter */
typedef struct {
double a0, a1, a2; /* numerator coefficients */
double b0, b1, b2; /* denominator coefficients */
} BIQUAD;
BIQUAD ProtoCoef[FILTER_SECTIONS]; /* Filter prototype coefficients,
1 for each filter section */
void szxform(
double *a0, double *a1, double *a2, /* numerator coefficients */
double *b0, double *b1, double *b2, /* denominator coefficients */
double fc, /* Filter cutoff frequency */
double fs, /* sampling rate */
double *k, /* overall gain factor */
float *coef); /* pointer to 4 iir coefficients */
/*
* --------------------------------------------------------------------
*
* iir_filter - Perform IIR filtering sample by sample on floats
*
* Implements cascaded direct form II second order sections.
* Requires FILTER structure for history and coefficients.
* The length in the filter structure specifies the number of sections.
* The size of the history array is 2*iir->length.
* The size of the coefficient array is 4*iir->length + 1 because
* the first coefficient is the overall scale factor for the filter.
* Returns one output sample for each input sample. Allocates history
* array if not previously allocated.
*
* float iir_filter(float input,FILTER *iir)
*
* float input new float input sample
* FILTER *iir pointer to FILTER structure
*
* Returns float value giving the current output.
*
* Allocation errors cause an error message and a call to exit.
* --------------------------------------------------------------------
*/
float iir_filter(input,iir)
float input; /* new input sample */
FILTER *iir; /* pointer to FILTER structure */
{
unsigned int i;
float *hist1_ptr,*hist2_ptr,*coef_ptr;
float output,new_hist,history1,history2;
/* allocate history array if different size than last call */
if(!iir->history) {
iir->history = (float *) calloc(2*iir->length,sizeof(float));
if(!iir->history) {
printf("\nUnable to allocate history array in iir_filter\n");
exit(1);
}
}
coef_ptr = iir->coef; /* coefficient pointer */
hist1_ptr = iir->history; /* first history */
hist2_ptr = hist1_ptr + 1; /* next history */
/* 1st number of coefficients array is overall input scale factor,
* or filter gain */
output = input * (*coef_ptr++);
for (i = 0 ; i < iir->length; i++)
{
history1 = *hist1_ptr; /* history values */
history2 = *hist2_ptr;
output = output - history1 * (*coef_ptr++);
new_hist = output - history2 * (*coef_ptr++); /* poles */
output = new_hist + history1 * (*coef_ptr++);
output = output + history2 * (*coef_ptr++); /* zeros */
*hist2_ptr++ = *hist1_ptr;
*hist1_ptr++ = new_hist;
hist1_ptr++;
hist2_ptr++;
}
return(output);
}
/*
* --------------------------------------------------------------------
*
* main()
*
* Example main function to show how to update filter coefficients.
* We create a 4th order filter (24 db/oct roloff), consisting
* of two second order sections.
* --------------------------------------------------------------------
*/
int main()
{
FILTER iir;
float *coef;
double fs, fc; /* Sampling frequency, cutoff frequency */
double Q; /* Resonance > 1.0 < 1000 */
unsigned nInd;
double a0, a1, a2, b0, b1, b2;
double k; /* overall gain factor */
/*
* Setup filter s-domain coefficients
*/
/* Section 1 */
ProtoCoef[0].a0 = 1.0;
ProtoCoef[0].a1 = 0;
ProtoCoef[0].a2 = 0;
ProtoCoef[0].b0 = 1.0;
ProtoCoef[0].b1 = 0.765367;
ProtoCoef[0].b2 = 1.0;
/* Section 2 */
ProtoCoef[1].a0 = 1.0;
ProtoCoef[1].a1 = 0;
ProtoCoef[1].a2 = 0;
ProtoCoef[1].b0 = 1.0;
ProtoCoef[1].b1 = 1.847759;
ProtoCoef[1].b2 = 1.0;
iir.length = FILTER_SECTIONS; /* Number of filter sections */
/*
* Allocate array of z-domain coefficients for each filter section
* plus filter gain variable
*/
iir.coef = (float *) calloc(4 * iir.length + 1, sizeof(float));
if (!iir.coef)
{
printf("Unable to allocate coef array, exiting\n");
exit(1);
}
k = 1.0; /* Set overall filter gain */
coef = iir.coef + 1; /* Skip k, or gain */
Q = 1; /* Resonance */
fc = 5000; /* Filter cutoff (Hz) */
fs = 44100; /* Sampling frequency (Hz) */
/*
* Compute z-domain coefficients for each biquad section
* for new Cutoff Frequency and Resonance
*/
for (nInd = 0; nInd < iir.length; nInd++)
{
a0 = ProtoCoef[nInd].a0;
a1 = ProtoCoef[nInd].a1;
a2 = ProtoCoef[nInd].a2;
b0 = ProtoCoef[nInd].b0;
b1 = ProtoCoef[nInd].b1 / Q; /* Divide by resonance or Q */
b2 = ProtoCoef[nInd].b2;
szxform(&a0, &a1, &a2, &b0, &b1, &b2, fc, fs, &k, coef);
coef += 4; /* Point to next filter section */
}
/* Update overall filter gain in coef array */
iir.coef[0] = k;
/* Display filter coefficients */
for (nInd = 0; nInd < (iir.length * 4 + 1); nInd++)
printf("C[%d] = %15.10f\n", nInd, iir.coef[nInd]);
/*
* To process audio samples, call function iir_filter()
* for each audio sample
*/
return (0);
}
// ----------------- file filterIIR00.c end -----------------
Reposting bilinear.c just in case the other one was not the latest version.
// ----------------- file bilinear.c begin -----------------
/*
* ----------------------------------------------------------
* bilinear.c
*
* Perform bilinear transformation on s-domain coefficients
* of 2nd order biquad section.
* First design an analog filter and use s-domain coefficients
* as input to szxform() to convert them to z-domain.
*
* Here's the butterworth polinomials for 2nd, 4th and 6th order sections.
* When we construct a 24 db/oct filter, we take to 2nd order
* sections and compute the coefficients separately for each section.
*
* n Polinomials
* --------------------------------------------------------------------
* 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)
*
* Where n is a filter order.
* For n=4, or two second order sections, we have following equasions for each
* 2nd order stage:
*
* (1 / (s^2 + (1/Q) * 0.765367s + 1)) * (1 / (s^2 + (1/Q) * 1.847759s + 1))
*
* Where Q is filter quality factor 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.
*
* The nominator part is just 1.
* The denominator coefficients for stage 1 of filter are:
* b2 = 1; b1 = 0.765367; b0 = 1;
* numerator is
* a2 = 0; a1 = 0; a0 = 1;
*
* The denominator coefficients for stage 1 of filter are:
* b2 = 1; b1 = 1.847759; b0 = 1;
* numerator is
* a2 = 0; a1 = 0; a0 = 1;
*
* These coefficients are used directly by the szxform()
* and bilinear() functions. For all stages the numerator
* is the same and the only thing that is different between
* different stages is 1st order coefficient. The rest of
* coefficients are the same for any stage and equal to 1.
*
* Any filter could be constructed using this approach.
*
* References:
* Van Valkenburg, "Analog Filter Design"
* Oxford University Press 1982
* ISBN 0-19-510734-9
*
* C Language Algorithms for Digital Signal Processing
* Paul Embree, Bruce Kimble
* Prentice Hall, 1991
* ISBN 0-13-133406-9
*
* Digital Filter Designer's Handbook
* With C++ Algorithms
* Britton Rorabaugh
* McGraw Hill, 1997
* ISBN 0-07-053806-9
* ----------------------------------------------------------
*/
#include <math.h>
void prewarp(double *a0, double *a1, double *a2, double fc, double fs);
void bilinear(
double a0, double a1, double a2, /* numerator coefficients */
double b0, double b1, double b2, /* denominator coefficients */
double *k, /* overall gain factor */
double fs, /* sampling rate */
float *coef); /* pointer to 4 iir coefficients */
/*
* ----------------------------------------------------------
* 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(
double *a0, double *a1, double *a2,
double fc, double fs)
{
double wp, pi;
pi = 4.0 * atan(1.0);
wp = 2.0 * fs * tan(pi * fc / fs);
*a2 = (*a2) / (wp * wp);
*a1 = (*a1) / wp;
}
/*
* ----------------------------------------------------------
* bilinear()
*
* Transform the numerator and denominator coefficients
* of s-domain biquad section into corresponding
* z-domain coefficients.
*
* Store the 4 IIR coefficients in array pointed by coef
* in following order:
* beta1, beta2 (denominator)
* alpha1, alpha2 (numerator)
*
* Arguments:
* a0-a2 - s-domain numerator coefficients
* b0-b2 - 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
* ----------------------------------------------------------
*/
void bilinear(
double a0, double a1, double a2, /* numerator coefficients */
double b0, double b1, double b2, /* denominator coefficients */
double *k, /* overall gain factor */
double fs, /* sampling rate */
float *coef /* pointer to 4 iir coefficients */
)
{
double ad, bd;
/* alpha (Numerator in s-domain) */
ad = 4. * a2 * fs * fs + 2. * a1 * fs + a0;
/* beta (Denominator in s-domain) */
bd = 4. * b2 * fs * fs + 2. * b1* fs + b0;
/* update gain constant for this section */
*k *= ad/bd;
/* Denominator */
*coef++ = (2. * b0 - 8. * b2 * fs * fs)
/ bd; /* beta1 */
*coef++ = (4. * b2 * fs * fs - 2. * b1 * fs + b0)
/ bd; /* beta2 */
/* Nominator */
*coef++ = (2. * a0 - 8. * a2 * fs * fs)
/ ad; /* alpha1 */
*coef = (4. * a2 * fs * fs - 2. * a1 * fs + a0)
/ ad; /* alpha2 */
}
/*
* ----------------------------------------------------------
* Transform from s to z domain using bilinear transform
* with prewarp.
*
* Arguments:
* For argument description look at bilinear()
*
* coef - pointer to array of floating point coefficients,
* corresponding to output of bilinear transofrm
* (z domain).
*
* Note: frequencies are in Hz.
* ----------------------------------------------------------
*/
void szxform(
double *a0, double *a1, double *a2, /* numerator coefficients */
double *b0, double *b1, double *b2, /* denominator coefficients */
double fc, /* Filter cutoff frequency */
double fs, /* sampling rate */
double *k, /* overall gain factor */
float *coef) /* pointer to 4 iir coefficients */
{
/* Calculate a1 and a2 and overwrite the original values */
prewarp(a0, a1, a2, fc, fs);
prewarp(b0, b1, b2, fc, fs);
bilinear(*a0, *a1, *a2, *b0, *b1, *b2, k, fs, coef);
}
// ----------------- file bilinear.c end -----------------
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Date this article was posted to GameDev.net: 11/18/1999
(Note that this date does not necessarily correspond to the date the article was written)
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