Hash :
056d0696
Author :
Thomas de Grivel
Date :
2020-02-10T14:30:45
Butterworth lowpass fourth order filter
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
/*
* Copyright 2020 Thomas de Grivel <thoxdg@gmail.com> +33614550127
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/* Butterworth lowpass fourth order filter
a: cos(5*%pi/8) $
b: cos(7*%pi/8) $
s: 2*F*(1-z)/(1+z) $
B4:((s/w)^2-2*(s/w)*a+1)*((s/w)^2-2*s/w*b+1) $
H: 1/B4 $
ratsimp(H);
4 4 4 3 4 2 4 4
(%o8) (w z + 4 w z + 6 w z + 4 w z + w )
4 3 2 2 2 3 3
/((w + (4 F b + 4 F a) w + (16 F a b + 8 F ) w + (16 F b + 16 F a) w
4 4 4 3 3 3
+ 16 F ) z + (4 w + (8 F b + 8 F a) w + ((- 32 F b) - 32 F a) w
4 3 4 2 2 2 4 2
- 64 F ) z + (6 w + ((- 32 F a b) - 16 F ) w + 96 F ) z
4 3 3 3 4 4
+ (4 w + ((- 8 F b) - 8 F a) w + (32 F b + 32 F a) w - 64 F ) z + w
3 2 2 2
+ ((- 4 F b) - 4 F a) w + (16 F a b + 8 F ) w
3 3 4
+ ((- 16 F b) - 16 F a) w + 16 F )
c: 16*F^4+( 16*b+16*a)*F^3*w+(16*a*b +8)*F^2*w^2+( 4*b+4*a)*F*w^3+ w^4 $
d: -64*F^4+(-32*b-32*a)*F^3*w +( 8*b+8*a)*F*w^3+4*w^4 $
e: 96*F^4 +(-32*a*b-16)*F^2*w^2 +6*w^4 $
f: -64*F^4+( 32*b+32*a)*F^3*w +(-8*b-8*a)*F*w^3+4*w^4 $
g: 16*F^4+(-16*b-16*a)*F^3*w+(16*a*b +8)*F^2*w^2+(-4*b-4*a)*F*w^3+ w^4 $
c: 16*F^4 + 16*(a+b)*F^3*w + (16*a*b+8)*F^2*w^2 + 4*(a+b)*F*w^3 + w^4 $
d: -(64*F^4 + 32*(a+b)*F^3*w) + 8*(a+b)*F*w^3 + 4*w^4 $
e: 96*F^4 -2*(16*a*b+8)*F^2*w^2 + 6*w^4 $
f: -64*F^4 + 32*(a+b)*F^3*w - 8*(a+b)*F*w^3 + 4*w^4 $
g: 16*F^4 - 16*(a+b)*F^3*w + (16*a*b+8)*F^2*w^2 - 4*(a+b)*F*w^3 + w^4 $
y: (w4*(x4+4*x3+6*x2+4*x1+x)-(c*y4+d*y3+e*y2+f*y1))/g $
*/
#include <math.h>
#include "rtbuf.h"
#include "rtbuf_signal.h"
int rtbuf_signal_lowpass4_start (s_rtbuf *rtb)
{
s_rtbuf_signal_lowpass4_data *data;
assert(rtb->proc->out_bytes == sizeof(*data));
data = (s_rtbuf_signal_lowpass4_data*) rtb->data;
data->x1 = 0.0;
data->x2 = 0.0;
data->x3 = 0.0;
data->x4 = 0.0;
data->y1 = 0.0;
data->y2 = 0.0;
data->y3 = 0.0;
data->y4 = 0.0;
return 0;
}
int rtbuf_signal_lowpass4 (s_rtbuf *rtb)
{
s_rtbuf_signal_fun in;
s_rtbuf_signal_fun cutoff;
s_rtbuf_signal_lowpass4_data *data;
unsigned int i = 0;
const double a = cos(5.0 * M_PI / 8.0);
const double b = cos(7.0 * M_PI / 8.0);
const double f = RTBUF_SIGNAL_SAMPLERATE;
const double _4a_bf = 4.0 * (a + b) * f;
const double f2 = f * f;
const double _16ab_8f2 = (16.0 * a * b + 8.0) * f2;
const double f3 = f2 * f;
const double _16a_bf3 = 16.0 * (a + b) * f3;
const double f4 = f2 * f2;
const double _16f4 = 16.0 * f4;
const double _64f4 = 64.0 * f4;
rtbuf_signal_fun(rtb, RTBUF_SIGNAL_LOWPASS_IN_SIGNAL, &in);
rtbuf_signal_fun(rtb, RTBUF_SIGNAL_LOWPASS_IN_CUTOFF, &cutoff);
data = (s_rtbuf_signal_lowpass4_data*) rtb->data;
while (i < RTBUF_SIGNAL_SAMPLES) {
const double x = in.sample_fun(in.signal, i);
const double fc = cutoff.sample_fun(cutoff.signal, i);
const double w = 2.0 * M_PI * fc;
const double _16a_bf3w = _16a_bf3 * w;
const double _32a_bf3w = 2.0 * _16a_bf3w;
const double w2 = w * w;
const double _16ab_8f2w2 = _16ab_8f2 * w2;
const double w3 = w2 * w;
const double _4a_bfw3 = _4a_bf * w3;
const double _8a_bfw3 = 2.0 * _4a_bfw3;
const double w4 = w2 * w2;
const double _4w4 = 4.0 * w4;
const double c = _16f4 + _16a_bf3w + _16ab_8f2w2 + _4a_bfw3 + w4;
const double d = -(_64f4 + _32a_bf3w) + _8a_bfw3 + _4w4;
const double e = 96.0 * f4 - 2.0 * _16ab_8f2w2 + 6.0 * w4;
const double f = - _64f4 + _32a_bf3w - _8a_bfw3 + _4w4;
const double g = _16f4 - _16a_bf3w + _16ab_8f2w2 - _4a_bfw3 + w4;
data->signal[i] = (w4 * (x
+ 4.0 * (data->x1 +
data->x3)
+ 6.0 * data->x2
+ data->x4)
- (c * data->y4
+ d * data->y3
+ e * data->y2
+ f * data->y1)) / g;
data->x4 = data->x3;
data->x3 = data->x2;
data->x2 = data->x1;
data->x1 = x;
data->y4 = data->y3;
data->y3 = data->y2;
data->y2 = data->y1;
data->y1 = data->signal[i];
i++;
}
return 0;
}