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//
// iirdes_example.c
//
// Tests infinite impulse response (IIR) digital filter design.
// SEE ALSO: iirdes_analog_example.c
// iir_filter_crcf_example.c
//
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <getopt.h>
#include <math.h>
#include "liquid.h"
#define OUTPUT_FILENAME "iirdes_example.m"
// print usage/help message
void usage()
{
printf("iirdes_example -- infinite impulse response filter design\n");
printf("options (default values in []):\n");
printf(" u/h : print usage/help\n");
printf(" t : filter type: [butter], cheby1, cheby2, ellip, bessel\n");
printf(" b : filter transformation: [LP], HP, BP, BS\n");
printf(" n : filter order, n > 0 [5]\n");
printf(" r : passband ripple in dB (cheby1, ellip), r > 0 [1.0]\n");
printf(" s : stopband attenuation in dB (cheby2, ellip), s > 0 [60.0]\n");
printf(" f : passband cut-off, 0 < f < 0.5 [0.2]\n");
printf(" c : center frequency (BP, BS cases), 0 < c < 0.5 [0.25]\n");
printf(" o : format [sos], tf\n");
printf(" sos : second-order sections form\n");
printf(" tf : regular transfer function form (potentially\n");
printf(" unstable for large orders\n");
}
int main(int argc, char*argv[]) {
// options
unsigned int order=5; // filter order
float fc = 0.20f; // cutoff frequency (low-pass prototype)
float f0 = 0.25f; // center frequency (band-pass, band-stop)
float As = 60.0f; // stopband attenuation [dB]
float Ap = 1.0f; // passband ripple [dB]
// filter type
liquid_iirdes_filtertype ftype = LIQUID_IIRDES_BUTTER;
// band type
liquid_iirdes_bandtype btype = LIQUID_IIRDES_LOWPASS;
// output format: second-order sections or transfer function
liquid_iirdes_format format = LIQUID_IIRDES_SOS;
int dopt;
while ((dopt = getopt(argc,argv,"uht:b:n:r:s:f:c:o:")) != EOF) {
switch (dopt) {
case 'u':
case 'h':
usage();
return 0;
case 't':
if (strcmp(optarg,"butter")==0) {
ftype = LIQUID_IIRDES_BUTTER;
} else if (strcmp(optarg,"cheby1")==0) {
ftype = LIQUID_IIRDES_CHEBY1;
} else if (strcmp(optarg,"cheby2")==0) {
ftype = LIQUID_IIRDES_CHEBY2;
} else if (strcmp(optarg,"ellip")==0) {
ftype = LIQUID_IIRDES_ELLIP;
} else if (strcmp(optarg,"bessel")==0) {
ftype = LIQUID_IIRDES_BESSEL;
} else {
fprintf(stderr,"error: iirdes_example, unknown filter type \"%s\"\n", optarg);
usage();
exit(1);
}
break;
case 'b':
if (strcmp(optarg,"LP")==0) {
btype = LIQUID_IIRDES_LOWPASS;
} else if (strcmp(optarg,"HP")==0) {
btype = LIQUID_IIRDES_HIGHPASS;
} else if (strcmp(optarg,"BP")==0) {
btype = LIQUID_IIRDES_BANDPASS;
} else if (strcmp(optarg,"BS")==0) {
btype = LIQUID_IIRDES_BANDSTOP;
} else {
fprintf(stderr,"error: iirdes_example, unknown band type \"%s\"\n", optarg);
usage();
exit(1);
}
break;
case 'n': order = atoi(optarg); break;
case 'r': Ap = atof(optarg); break;
case 's': As = atof(optarg); break;
case 'f': fc = atof(optarg); break;
case 'c': f0 = atof(optarg); break;
case 'o':
if (strcmp(optarg,"sos")==0) {
format = LIQUID_IIRDES_SOS;
} else if (strcmp(optarg,"tf")==0) {
format = LIQUID_IIRDES_TF;
} else {
fprintf(stderr,"error: iirdes_example, unknown output format \"%s\"\n", optarg);
usage();
exit(1);
}
break;
default:
exit(1);
}
}
// validate input
if (fc <= 0 || fc >= 0.5) {
fprintf(stderr,"error: %s, cutoff frequency out of range\n", argv[0]);
usage();
exit(1);
} else if (f0 < 0 || f0 > 0.5) {
fprintf(stderr,"error: %s, center frequency out of range\n", argv[0]);
usage();
exit(1);
} else if (Ap <= 0) {
fprintf(stderr,"error: %s, pass-band ripple out of range\n", argv[0]);
usage();
exit(1);
} else if (As <= 0) {
fprintf(stderr,"error: %s, stop-band ripple out of range\n", argv[0]);
usage();
exit(1);
}
// derived values : compute filter length
unsigned int N = order; // effective order
// filter order effectively doubles for band-pass, band-stop
// filters due to doubling the number of poles and zeros as
// a result of filter transformation
if (btype == LIQUID_IIRDES_BANDPASS ||
btype == LIQUID_IIRDES_BANDSTOP)
{
N *= 2;
}
unsigned int r = N % 2; // odd/even order
unsigned int L = (N-r)/2; // filter semi-length
// allocate memory for filter coefficients
unsigned int h_len = (format == LIQUID_IIRDES_SOS) ? 3*(L+r) : N+1;
float b[h_len];
float a[h_len];
// design filter
liquid_iirdes(ftype, btype, format, order, fc, f0, Ap, As, b, a);
// open output file
FILE*fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"n=%u;\n", order);
fprintf(fid,"r=%u;\n", r);
fprintf(fid,"L=%u;\n", L);
fprintf(fid,"nfft=1024;\n");
unsigned int i;
if (format == LIQUID_IIRDES_TF) {
// print coefficients
for (i=0; i<=N; i++) printf("a[%3u] = %12.8f;\n", i, a[i]);
for (i=0; i<=N; i++) printf("b[%3u] = %12.8f;\n", i, b[i]);
fprintf(fid,"a = zeros(1,n+1);\n");
fprintf(fid,"b = zeros(1,n+1);\n");
for (i=0; i<=N; i++) {
fprintf(fid,"a(%3u) = %12.4e;\n", i+1, a[i]);
fprintf(fid,"b(%3u) = %12.4e;\n", i+1, b[i]);
}
fprintf(fid,"\n");
fprintf(fid,"H = fft(b,nfft)./fft(a,nfft);\n");
fprintf(fid,"H = fftshift(H);\n");
fprintf(fid,"%% group delay\n");
fprintf(fid,"c = conv(b,fliplr(conj(a)));\n");
fprintf(fid,"cr = c.*[0:(length(c)-1)];\n");
fprintf(fid,"t0 = fftshift(fft(cr,nfft));\n");
fprintf(fid,"t1 = fftshift(fft(c, nfft));\n");
fprintf(fid,"polebins = find(abs(t1)<1e-6);\n");
fprintf(fid,"t0(polebins)=0;\n");
fprintf(fid,"t1(polebins)=1;\n");
fprintf(fid,"gd = real(t0./t1) - length(a) + 1;\n");
} else {
float * B = b;
float * A = a;
// print coefficients
printf("B [%u x 3] :\n", L+r);
for (i=0; i<L+r; i++)
printf(" %12.8f %12.8f %12.8f\n", B[3*i+0], B[3*i+1], B[3*i+2]);
printf("A [%u x 3] :\n", L+r);
for (i=0; i<L+r; i++)
printf(" %12.8f %12.8f %12.8f\n", A[3*i+0], A[3*i+1], A[3*i+2]);
unsigned int j;
for (i=0; i<L+r; i++) {
for (j=0; j<3; j++) {
fprintf(fid,"B(%3u,%3u) = %16.8e;\n", i+1, j+1, B[3*i+j]);
fprintf(fid,"A(%3u,%3u) = %16.8e;\n", i+1, j+1, A[3*i+j]);
}
}
fprintf(fid,"\n");
fprintf(fid,"H = ones(1,nfft);\n");
fprintf(fid,"gd = zeros(1,nfft);\n");
fprintf(fid,"t0 = zeros(1,nfft);\n");
fprintf(fid,"t1 = zeros(1,nfft);\n");
fprintf(fid,"for i=1:(L+r),\n");
fprintf(fid," H = H .* fft(B(i,:),nfft)./fft(A(i,:),nfft);\n");
fprintf(fid," %% group delay\n");
fprintf(fid," c = conv(B(i,:),fliplr(conj(A(i,:))));\n");
fprintf(fid," cr = c.*[0:4];\n");
fprintf(fid," t0 = fftshift(fft(cr,nfft));\n");
fprintf(fid," t1 = fftshift(fft(c, nfft));\n");
fprintf(fid," polebins = find(abs(t1)<1e-6);\n");
fprintf(fid," t0(polebins)=0;\n");
fprintf(fid," t1(polebins)=1;\n");
fprintf(fid," gd = gd + real(t0./t1) - 2;\n");
fprintf(fid,"end;\n");
fprintf(fid,"H = fftshift(H);\n");
}
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"figure;\n");
// plot magnitude response (detail)
fprintf(fid,"subplot(3,1,1),\n");
fprintf(fid," plot(f,20*log10(abs(H)),'-','Color',[0.5 0 0],'LineWidth',2);\n");
fprintf(fid," axis([0.0 0.5 -4 1]);\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('Normalized Frequency');\n");
fprintf(fid," ylabel('Filter PSD [dB]');\n");
// plot magnitude response (full range)
fprintf(fid,"subplot(3,1,2),\n");
fprintf(fid," plot(f,20*log10(abs(H)),'-','Color',[0.5 0 0],'LineWidth',2);\n");
fprintf(fid," axis([0.0 0.5 -100 10]);\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('Normalized Frequency');\n");
fprintf(fid," ylabel('Filter PSD [dB]');\n");
// plot group delay
fprintf(fid,"subplot(3,1,3);\n");
fprintf(fid," plot(f,gd,'-','Color',[0 0.5 0],'LineWidth',2);\n");
fprintf(fid," axis([0.0 0.5 0 ceil(1.1*max(gd))]);\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('Normalized Frequency');\n");
fprintf(fid," ylabel('Group delay [samples]');\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
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