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iir.c
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iir.c
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/**************************************************************************/
/*!
@file iir.c
@brief Helper functions for IIR filters generated with Octave or
Matlab (supports 1, 2 or 3-pole filters)
@note Shamelessly taken from Holly Gates tutorial on using Octave
to calculate IIR/FIR filters:
http://tooling-up.blogspot.fr/2013/06/signal-acquisition-filtering-on-simple.html
*/
/**************************************************************************/
#include "iir.h"
#include <math.h>
#define IIR_PI 3.14159265358979323846
/**************************************************************************/
/*!
@brief Single pole IIR filter routine
@param[in] filt
Pointer to the iir_filt_1p_instance instance containing
the filter settings
@param[in] in
The single-precision floating point value to feed into
the filter
@returns The single-precision floating point filter output
@code
float32_t filtered = 0.0F;
// Setup the single-pole filter values
iir_filt_1p_instance iir = { .a1=0.1F,
.b0=0.9F, .b1=0.9F };
// Pass some data into the filter
filtered = iir_filt_1p(&iir, 12.345F);
@endcode
*/
/**************************************************************************/
float32_t iir_filt_1p(iir_filt_1p_instance* filt, float32_t in)
{
/* Calculate new output */
filt->out = (filt->b0*in + filt->b1*filt->x1 - filt->a1*filt->y1);
/* Shift input samples */
filt->x1 = in;
/* Shift output samples */
filt->y1 = filt->out;
return(filt->out);
}
/**************************************************************************/
/*!
@brief Two pole IIR filter routine
For a two pole butterworth filter, use the iis_butter2
function in this file to calculate the butterworth filter
coefficients without having to make use of Octave.
@param[in] filt
Pointer to the iir_filt_2p_instance instance containing
the filter settings
@param[in] in
The single-precision floating point value to feed into
the filter
@returns The single-precision floating point filter output
@code
// Calculate a second order butterworth filter with the following
// characteristics:
//
// Fc = 10Hz - Cutoff Frequency
// Fs = 1000Hz - Sample Rate
//
// Enter the following in Octave:
//
// [bb2 ba2] = butter(2, 10/500);
//
// Where: 2 = second order filter (3=third order, etc.)
// 10 = Fc
// 500 = Fnyq (1/2 Fs)
//
// Visualise the results (sanity check):
//
// freqz(bb2,ba2)
//
// Get our values (enter 'bb2 and 'ba2'):
//
// bb2 =
//
// 9.4469e-004 1.8894e-003 9.4469e-004
//
// ba2 =
//
// 1.00000 -1.91120 0.91498
// Setup the 2 pole butterworth filter with values calculated above
iir_filt_2p_instance iir_butter = { .a1=-1.91120F, .a2=0.91498F,
.b0=9.4469e-004, .b1=1.8894e-003, .b2=9.4469e-004 };
float32_t i, filtered;
i = filtered = 0.0F;
while (1)
{
// ToDo: Get ADC at the right frequency (Fs above)
i++;
// Apply the digital filter
filtered = iir_filt_2p(&iir_butter, i);
debug_printf("%f\n", filtered);
}
@endcode
*/
/**************************************************************************/
float32_t iir_filt_2p(iir_filt_2p_instance* filt, float32_t in)
{
/* Calculate new output */
filt->out = (filt->b0*in +
filt->b1*filt->x1 + filt->b2*filt->x2 -
filt->a1*filt->y1 - filt->a2*filt->y2);
/* Shift input samples */
filt->x2 = filt->x1;
filt->x1 = in;
/* Shift output samples */
filt->y2 = filt->y1;
filt->y1 = filt->out;
return(filt->out);
}
/**************************************************************************/
/*!
@brief Two pole integer based IIR filter routine
@param[in] filt
Pointer to the iir_filt_i_2p_instance instance containing
the filter settings
@param[in] in
The int32_t value to feed into the filter
@returns The int32_t filter output
@code
ToDo
@endcode
*/
/**************************************************************************/
int32_t iir_filt_i_2p(iir_filt_i_2p_instance* filt, int32_t in)
{
/* Calculate new output */
filt->out = (filt->b0*in +
filt->b1*filt->x1 + filt->b2*filt->x2)>>(filt->bf);
filt->out -= ((filt->a1*filt->y1 + filt->a2*filt->y2)>>(filt->af));
/* Shift input samples */
filt->x2 = filt->x1;
filt->x1 = in;
/* Shift output samples */
filt->y2 = filt->y1;
filt->y1 = filt->out;
return(filt->out);
}
/**************************************************************************/
/*!
@brief Three pole IIR filter routine
@param[in] filt
Pointer to the iir_filt_3p_instance instance containing
the filter settings
@param[in] in
The single-precision floating point value to feed into
the filter
@returns The single-precision floating point filter output
@code
// Setup the 3 pole filter with values from Octave/Matlab
iir_filt_3p_instance iir_filt = {
.a1=-2.93717, .a2=2.87630, .a3=-0.93910,
.b0=3.0044e-5, .b1=0.00000, .b2=0.00000, .b3=0.00000
};
float32_t in, filtered;
in = filtered = 0.0F;
while (1)
{
// ToDo: Read the ADC, etc., and populate 'in'
in++;
// Apply the digital filter
filtered = iir_filt_3p(&iir_filt, i);
printf("%f\n", filtered);
}
@endcode
*/
/**************************************************************************/
float32_t iir_filt_3p(iir_filt_3p_instance* filt, float32_t in)
{
/* Calculate new output */
filt->out = (filt->b0*in +
filt->b1*filt->x1 + filt->b2*filt->x2 + filt->b3*filt->x3 -
filt->a1*filt->y1 - filt->a2*filt->y2 - filt->a3*filt->y3);
/* Shift input samples */
filt->x3 = filt->x2;
filt->x2 = filt->x1;
filt->x1 = in;
/* Shift output samples */
filt->y3 = filt->y2;
filt->y2 = filt->y1;
filt->y1 = filt->out;
return(filt->out);
}
/**************************************************************************/
/*!
@brief Four pole IIR filter routine
@param[in] filt
Pointer to the iir_filt_4p_instance instance containing
the filter settings
@param[in] in
The single-precision floating point value to feed into
the filter
@returns The single-precision floating point filter output
*/
/**************************************************************************/
float32_t iir_filt_4p(iir_filt_4p_instance* filt, float32_t in)
{
/* Calculate new output */
filt->out = (filt->b0*in +
filt->b1*filt->x1 + filt->b2*filt->x2 + filt->b3*filt->x3 + filt->b4*filt->x4 -
filt->a1*filt->y1 - filt->a2*filt->y2 - filt->a3*filt->y3 - filt->a4*filt->y4);
/* Shift input samples */
filt->x4 = filt->x3;
filt->x3 = filt->x2;
filt->x2 = filt->x1;
filt->x1 = in;
/* Shift output samples */
filt->y4 = filt->y3;
filt->y3 = filt->y2;
filt->y2 = filt->y1;
filt->y1 = filt->out;
return(filt->out);
}
/**************************************************************************/
/*!
@brief Two pole butterworth low pass IIR filter coefficient
generator routine
@param[in] filt
Pointer to the iir_filt_2p_instance instance containing
the filter data structure
@param[in] fs
sampling frequency
@param[in] fc
cut point frequency
@code
iir_filt_2p_instance test_filt; // The filter structure itself
float fs = 100; // 100Hz sample frequency
float fc = 5; // 5Hz cut frequency
float input,output;
iir_butter2(&test_filt,fs,fc); // Generate the filter coeffs
printf("filter coeffs:\r\n");
printf("test_filt a1:%f a2:%f b0:%f b1:%f b2:%f\r\n",
test_filt.a1,test_filt.a2,test_filt.b0,test_filt.b1,test_filt.b2);
input = 10.0;
output = iir_filt_2p(&test_filt,input); // Run the filter once
// Note: You need to run the filter at the frequency you specified for Fs!
printf("input:%f output:%f\r\n", input, output);
@endcode
You can verify the output of this filter against Octave as follows:
OUTPUT at terminal when run with fs=100 fc=5
-------------------------------
filter coeffs:
test_filt a1:-1.561018 a2:0.641352 b0:0.020083 b1:0.040167 b2:0.020083
input:10.000000 output:0.200834
OCTAVE design: 2 pole, fc=5, fs=50 (Fnyq = 1/2 Fs)
-------------------------------
octave:4> pkg load signal
octave:5> [b a] = butter(2,5/50)
b =
0.020083 0.040167 0.020083
a =
1.00000 -1.56102 0.64135
*/
/**************************************************************************/
void iir_butter2(iir_filt_2p_instance* filt, float32_t fs, float32_t fc)
{
float ax = tan(IIR_PI*fc/fs);
float ax2 = ax*ax;
float r = sin(IIR_PI*3.0/4.0);
float sx = ax2 + 2.0*ax*r + 1.0;
float A = ax2/sx;
float d1 = 2.0*(1-ax2)/sx;
float d2 = -(ax2 - 2.0*ax*r + 1.0)/sx;
filt->b0 = A;
filt->b1 = 2*A;
filt->b2 = A;
filt->a1 = -1*d1;
filt->a2 = -1*d2;
}