Add ability to compute filter response
Adds functionality to compute the response of the filter's transfer function at a given frequency. This uses the Z domain transform. A new test program zplot_filter (which is compatible with the existing plot_filter) is provided.
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@ -9,6 +9,7 @@
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#define HEADER_libiir
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/* standard includes, or includes needed for type declarations */
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#include <complex.h>
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/* options for text editors
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kate: replace-trailing-space-save true; space-indent true; tab-width 4;
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@ -0,0 +1,71 @@
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/* libiir/src/libiir/500_response.c
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*
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* Copyright: ©2011, Laurence Withers.
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* Author: Laurence Withers <l@lwithers.me.uk>
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* License: GPLv3
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*/
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static double complex
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iir_response_aux(int nc, const double* c, int nd, const double* d, double freq)
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{
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int i;
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double complex sum, resp, N;
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/* Z transform; substitutions:
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*
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* z = exp(jω)
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* where j is the imaginary unit (written as I in the C code below)
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* and where ω = 2πf
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*
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* z^-n = exp(jωn)
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*
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* exp(jx) = cos(x) + j.sin(x)
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*
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* z^-n = cos(-ωn) + j.sin(-ωn)
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*
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* N = -ω = -2πf
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*/
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N = -2 * M_PI * freq;
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sum = 0;
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for(i = 0; i < nc; ++i) {
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sum += c[i] * (cos(i*N) + I * sin(i*N));
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}
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resp = sum;
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sum = 1;
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for(i = 1; i <= nd; ++i) {
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sum += d[i - 1] * (cos(i*N) + I * sin(i*N));
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}
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return resp / sum;
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}
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double complex
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iir_response_c(const struct iir_coeff_t* coeff, double freq)
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{
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return iir_response_aux(coeff->nc, coeff->c, coeff->nd, coeff->d, freq);
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}
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double complex
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iir_response(const struct iir_filter_t* fi, double freq)
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{
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double complex resp;
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for(resp = 1.0; fi; fi = fi->next) {
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resp *= iir_response_aux(fi->nc, fi->c, fi->nd, fi->d, freq);
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}
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return resp;
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}
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/* options for text editors
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vim: expandtab:ts=4:sw=4
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*/
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@ -0,0 +1,52 @@
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/* libiir/src/libiir/500_response.h
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*
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* Copyright: ©2011, Laurence Withers.
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* Author: Laurence Withers <l@lwithers.me.uk>
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* License: GPLv3
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*/
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/*! \defgroup response Measuring IIR response
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These functions allow measuring the IIR response (i.e. frequency and phase of
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the transfer function) at a given frequency. The response is a complex number;
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see \c complex(5) for details. The magnitude \c cabs(z) is the gain of the
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filter and the phase \c carg(z) its phase delay.
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*/
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/*!@{*/
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/*! \brief Find response of coefficients at a single frequency.
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\param coeff Set of coefficients.
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\param freq Frequency of interest, as a fraction of sample rate.
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\returns Response as complex number.
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*/
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double complex iir_response_c(const struct iir_coeff_t* coeff, double freq);
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/*! \brief Find response of filter at a single frequency.
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\param fi Filter to evaluate.
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\param freq Frequency of interest, as a fraction of sample rate.
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\returns Response as a complex number.
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Similar to \ref iir_response_c(), except that it works on an instantiated
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filter (and takes all parts of a chained filter into account). Does not alter
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the state of the filter in any way and calls may be interleaved with filter
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evaluation.
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*/
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double complex iir_response(const struct iir_filter_t* fi, double freq);
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/*!@}*/
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/* options for text editors
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vim: expandtab:ts=4:sw=4:syntax=c.doxygen
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*/
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/* libiir/src/tests/zplot_filter.c
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*
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* Copyright: ©2010–2011, Laurence Withers.
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* Author: Laurence Withers <l@lwithers.me.uk>
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* License: GPLv3
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*/
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#include "iir.h"
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#include <math.h>
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#include <ctype.h>
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#include <errno.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <unistd.h>
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#include <complex.h>
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#define NPOINTS (1000)
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#define STEADY_STATE_CYCLES (20)
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char* tmp_fname;
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void
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unlink_tmpfile(void)
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{
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unlink(tmp_fname);
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}
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int
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do_plot(const char* filter_desc, double samp_rat, const char* png_filename)
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{
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int fd, ret;
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FILE* fp;
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char cmd_file[] = "/tmp/libiir-plot_filter.cmd.XXXXXX",
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cmd[200];
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fd = mkstemp(cmd_file);
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if(fd == -1) {
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perror("mkstemp");
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return -1;
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}
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fp = fdopen(fd, "w");
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fprintf(fp, "set terminal png size 1000,1000\n"
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"set output '%s'\n"
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"set multiplot layout 2,1 title \"Bode plot for filter '",
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png_filename);
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ret = 0;
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while(*filter_desc) {
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if(isspace(*filter_desc)) {
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if(!ret) {
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ret = 1;
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putc('\n', fp);
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}
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} else {
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putc(*filter_desc, fp);
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}
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++filter_desc;
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}
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fprintf(fp, "' at %fHz\"\n"
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"set grid\n"
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"set logscale\n"
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"set ytics add ('-3dB' %f)\n"
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"set xlabel 'Frequency (Hz)'\n"
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"set ylabel 'Gain'\n"
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"plot '%s' using 1:2 notitle\n"
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"unset logscale y\n"
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"set yrange [-180:180]\n"
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"set ytics -180,45,180\n"
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"set ylabel 'Phase (degrees)'\n"
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"plot '%s' using 1:3 notitle\n",
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samp_rat,
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pow(10, -3.0/20),
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tmp_fname,
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tmp_fname);
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fclose(fp);
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snprintf(cmd, sizeof(cmd), "gnuplot %s", cmd_file);
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ret = system(cmd);
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unlink(cmd_file);
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return ret;
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}
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double
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interp(int step, int max, double start, double end)
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{
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return start + step * ((end - start) / (max - 1));
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}
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void
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calc_response(FILE* fp,
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const struct iir_filter_t* fi,
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double samp_rat,
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double start_freq,
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double end_freq)
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{
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int step;
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double freq;
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double complex resp;
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for(step = 0; step < NPOINTS; ++step) {
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freq = exp(interp(step, NPOINTS, log(start_freq), log(end_freq)));
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resp = iir_response(fi, freq / samp_rat);
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fprintf(fp, "%e\t%e\t% 6.2f\n",
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freq,
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cabs(resp),
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carg(resp) * 180 / M_PI);
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}
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}
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int
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safe_strtod(const char* str, double* d)
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{
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char* endp = 0;
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errno = 0;
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*d = strtod(str, &endp);
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if(errno || !endp || *endp) return -1;
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return 0;
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}
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int
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main(int argc, char* argv[])
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{
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int fd;
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double samp_rat, start_freq, end_freq;
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FILE* fp;
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struct iir_filter_t* fi;
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/* process commandline arguments */
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if(argc == 2 && !strcmp(argv[1], "--print-summary")) {
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fputs("Generates Bode plot for a filter.\n", stdout);
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return 0;
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}
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if(argc != 6) {
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fputs("Usage: plot_filter 'filter_desc' samp_rat start_freq end_freq out.png\n",
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stderr);
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return 1;
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}
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fi = iir_parse(argv[1]);
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if(!fi) {
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fputs("Invalid filter description string.\n", stderr);
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return 1;
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}
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if(safe_strtod(argv[2], &samp_rat) || samp_rat < 1e-6) {
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fputs("Invalid sample rate. Positive float in Hz.\n", stderr);
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return 1;
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}
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if(safe_strtod(argv[3], &start_freq) || start_freq < 1e-6) {
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fputs("Invalid start frequency. Positive float in Hz.\n", stderr);
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return 1;
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}
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if(safe_strtod(argv[4], &end_freq) || end_freq < 1e-6
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|| end_freq > samp_rat || end_freq < start_freq)
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{
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fputs("Invalid end frequency. Positive float in Hz, less than sample\n"
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"rate, but greater than start frequency.\n", stderr);
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return 1;
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}
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printf("DC response: %f\n", cabs(iir_response(fi, 0)));
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/* create temporary file for results; gnuplot will use this */
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tmp_fname = strdup("/tmp/libiir-plot_filter.data.XXXXXX");
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fd = mkstemp(tmp_fname);
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if(fd == -1) {
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perror("mkstemp");
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return 1;
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}
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atexit(unlink_tmpfile);
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fp = fdopen(fd, "w");
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calc_response(fp, fi, samp_rat, start_freq, end_freq);
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fclose(fp);
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/* clean up (for valgrind) */
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iir_filter_free(fi);
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/* draw the plot */
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return do_plot(argv[1], samp_rat, argv[5]);
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}
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/* options for text editors
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kate: replace-trailing-space-save true; space-indent true; tab-width 4;
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vim: expandtab:ts=4:sw=4
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*/
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