// liquid_filter_crosscorr()
//
// Compute cross-correlation of two filters at a specific lag.
//
// _h : filter coefficients [size: _h_len]
// _h_len : filter length
// _g : filter coefficients [size: _g_len]
// _g_len : filter length
// _lag : cross-correlation lag (samples)
float liquid_filter_crosscorr(float * _h,
unsigned int _h_len,
float * _g,
unsigned int _g_len,
int _lag)
{
// cross-correlation is odd symmetric
if (_h_len < _g_len) {
return liquid_filter_crosscorr(_g, _g_len,
_h, _h_len,
-_lag);
}
// at this point _h_len > _g_len
// assert(_h_len > _g_len);
if (_lag <= -(int)_g_len) return 0.0f;
if (_lag >= (int)_h_len) return 0.0f;
int ig = _lag < 0 ? -_lag : 0; // starting index for _g
int ih = _lag > 0 ? _lag : 0; // starting index for _h
// compute length of overlap
// condition 1: condition 2: condition 3:
// [------ h ------] [------ h ------] [------ h ------]
// [-- g --] [-- g --] [-- g --]
// >| n |< >| n |< >| n |<
//
int n;
if (_lag < 0)
n = (int)_g_len + _lag;
else if (_lag < (_h_len-_g_len))
n = _g_len;
else
n = _h_len - _lag;
// compute cross-correlation
float rxy=0.0f; // initialize auto-correlation to zero
int i;
for (i=0; i< n; i++)
rxy += _h[ih+i] * _g[ig+i];
return rxy;
}
int main(int argc, char*argv[]) {
// options
unsigned int k=4; // filter samples/symbol
unsigned int m=3; // filter delay [symbols]
float beta = 0.3f; // filter excess bandwidth factor
// read properties from command line
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:")) != EOF) {
switch (dopt) {
case 'u':
case 'h': usage(); return 0;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: %s, k must be at least 2\n", argv[0]);
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: %s, m must be at least 1\n", argv[0]);
exit(1);
} else if (beta <= 0.0f || beta >= 1.0f) {
fprintf(stderr,"error: %s, beta must be in (0,1)\n", argv[0]);
exit(1);
}
unsigned int i;
// derived values
unsigned int h_len = 2*k*m+1; // filter length
// arrays
float ht[h_len]; // transmit filter coefficients
float hr[h_len]; // recieve filter coefficients
//
// start of filter design procedure
//
float H_prime[h_len]; // frequency response of Nyquist filter
float complex h_tx[h_len]; // impulse response of square-root Nyquist filter
float complex H_tx[h_len]; // frequency response of square-root Nyquist filter
// compute frequency response of Nyquist filter
for (i=0; i<h_len; i++) {
float f = (float)i / (float)h_len;
if (f > 0.5f) f = f - 1.0f;
H_prime[i] = firdes_freqresponse_fexp(f,k,beta);
}
// compute square-root response, copy to fft input
for (i=0; i<h_len; i++)
H_tx[i] = sqrtf(H_prime[i]);
// compute ifft and copy response
fft_run(h_len, H_tx, h_tx, LIQUID_FFT_BACKWARD, 0);
for (i=0; i<h_len; i++)
ht[i] = crealf( h_tx[(i+k*m+1)%h_len] ) / (float)(h_len);
// copy receive...
for (i=0; i<h_len; i++)
hr[i] = ht[i];
#if 0
// print results
for (i=0; i<h_len; i++)
printf("H_prime(%3u) = %12.8f;\n", i+1, H_prime[i]);
#endif
//
// end of filter design procedure
//
// print results to screen
printf("fexp receive filter:\n");
for (i=0; i<h_len; i++)
printf(" hr(%3u) = %12.8f;\n", i+1, hr[i]);
// compute isi
float rxy0 = liquid_filter_crosscorr(ht,h_len, hr,h_len, 0);
float isi_rms = 0.0f;
for (i=1; i<2*m; i++) {
float e = liquid_filter_crosscorr(ht,h_len, hr,h_len, i*k) / rxy0;
isi_rms += e*e;
}
isi_rms = sqrtf(isi_rms / (float)(2*m-1));
printf("\n");
printf("ISI (RMS) = %12.8f dB\n", 20*log10f(isi_rms));
//
// export 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\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"beta = %f;\n", beta);
fprintf(fid,"h_len = 2*k*m+1;\n");
fprintf(fid,"nfft = 1024;\n");
fprintf(fid,"ht = zeros(1,h_len);\n");
fprintf(fid,"hp = zeros(1,h_len);\n");
fprintf(fid,"hr = zeros(1,h_len);\n");
// print results
for (i=0; i<h_len; i++) fprintf(fid,"ht(%3u) = %12.4e;\n", i+1, ht[i]);
for (i=0; i<h_len; i++) fprintf(fid,"hr(%3u) = %12.4e;\n", i+1, hr[i]);
fprintf(fid,"hc = k*conv(ht,hr);\n");
// plot results
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"Ht = 20*log10(abs(fftshift(fft(ht, nfft))));\n");
fprintf(fid,"Hr = 20*log10(abs(fftshift(fft(hr, nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc/k,nfft))));\n");
fprintf(fid,"\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Ht,'LineWidth',1,'Color',[0.00 0.25 0.50],...\n");
fprintf(fid," f,Hr,'LineWidth',1,'Color',[0.00 0.50 0.25],...\n");
fprintf(fid," f,Hc,'LineWidth',2,'Color',[0.50 0.00 0.00],...\n");
fprintf(fid," [-0.5/k 0.5/k], [1 1]*20*log10(0.5),'or');\n");
fprintf(fid,"legend('transmit','receive','composite','alias points',1);\n");
fprintf(fid,"xlabel('Normalized Frequency');\n");
fprintf(fid,"ylabel('PSD');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([-0.5 0.5 -100 20]);\n");
fprintf(fid,"\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tr = [ -k*m:k*m]/k;\n");
fprintf(fid,"tc = [-2*k*m:2*k*m]/k;\n");
fprintf(fid,"ic = [0:k:(4*k*m)]+1;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(tr,ht,'-x', tr,hr,'-x');\n");
fprintf(fid," legend('transmit','receive',1);\n");
fprintf(fid," xlabel('Time');\n");
fprintf(fid," ylabel('fexp Tx/Rx Filters');\n");
fprintf(fid," grid on;\n");
fprintf(fid," axis([-2*m 2*m floor(5*min([hr ht]))/5 ceil(5*max([hr ht]))/5]);\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(tc,hc,'-x', tc(ic),hc(ic),'or');\n");
fprintf(fid," xlabel('Time');\n");
fprintf(fid," ylabel('fexp Composite Response');\n");
fprintf(fid," grid on;\n");
fprintf(fid," axis([-2*m 2*m -0.2 1.2]);\n");
fprintf(fid," axis([-2*m 2*m floor(5*min(hc))/5 ceil(5*max(hc))/5]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
return 0;
}
int main(int argc, char*argv[]) {
// options
unsigned int k=4; // samples/symbol
unsigned int m=3; // filter delay [symbols]
float BT = 0.3f; // bandwidth-time product
// read properties from command line
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:")) != EOF) {
switch (dopt) {
case 'u':
case 'h': usage(); return 0;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': BT = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: %s, k must be at least 2\n", argv[0]);
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: %s, m must be at least 1\n", argv[0]);
exit(1);
} else if (BT <= 0.0f || BT >= 1.0f) {
fprintf(stderr,"error: %s, BT must be in (0,1)\n", argv[0]);
exit(1);
}
unsigned int i;
// derived values
unsigned int h_len = 2*k*m+1; // filter length
// arrays
float ht[h_len]; // transmit filter coefficients
float hr[h_len]; // recieve filter coefficients
// design transmit filter
liquid_firdes_gmsktx(k,m,BT,0.0f,ht);
// print results to screen
printf("gmsk transmit filter:\n");
for (i=0; i<h_len; i++)
printf(" ht(%3u) = %12.8f;\n", i+1, ht[i]);
//
// start of filter design procedure
//
float beta = BT; // prototype filter cut-off
float delta = 1e-2f; // filter design correction factor
// temporary arrays
float h_primef[h_len]; // temporary buffer for real coefficients
float g_primef[h_len]; //
float complex h_tx[h_len]; // impulse response of transmit filter
float complex h_prime[h_len]; // impulse response of 'prototype' filter
float complex g_prime[h_len]; // impulse response of 'gain' filter
float complex h_hat[h_len]; // impulse response of receive filter
float complex H_tx[h_len]; // frequency response of transmit filter
float complex H_prime[h_len]; // frequency response of 'prototype' filter
float complex G_prime[h_len]; // frequency response of 'gain' filter
float complex H_hat[h_len]; // frequency response of receive filter
// create 'prototype' matched filter
// for now use raised-cosine
liquid_firdes_nyquist(LIQUID_NYQUIST_RCOS,k,m,beta,0.0f,h_primef);
// create 'gain' filter to improve stop-band rejection
float fc = (0.7f + 0.1*beta) / (float)k;
float As = 60.0f;
liquid_firdes_kaiser(h_len, fc, As, 0.0f, g_primef);
// copy to fft input buffer, shifting appropriately
for (i=0; i<h_len; i++) {
h_prime[i] = h_primef[ (i+k*m)%h_len ];
g_prime[i] = g_primef[ (i+k*m)%h_len ];
h_tx[i] = ht[ (i+k*m)%h_len ];
}
// run ffts
fft_run(h_len, h_prime, H_prime, FFT_FORWARD, 0);
fft_run(h_len, g_prime, G_prime, FFT_FORWARD, 0);
fft_run(h_len, h_tx, H_tx, FFT_FORWARD, 0);
#if 0
// print results
for (i=0; i<h_len; i++)
printf("Ht(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(H_tx[i]), cimagf(H_tx[i]));
for (i=0; i<h_len; i++)
printf("H_prime(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(H_prime[i]), cimagf(H_prime[i]));
for (i=0; i<h_len; i++)
printf("G_prime(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(G_prime[i]), cimagf(G_prime[i]));
#endif
// find minimum of reponses
float H_tx_min = 0.0f;
float H_prime_min = 0.0f;
float G_prime_min = 0.0f;
for (i=0; i<h_len; i++) {
if (i==0 || crealf(H_tx[i]) < H_tx_min) H_tx_min = crealf(H_tx[i]);
if (i==0 || crealf(H_prime[i]) < H_prime_min) H_prime_min = crealf(H_prime[i]);
if (i==0 || crealf(G_prime[i]) < G_prime_min) G_prime_min = crealf(G_prime[i]);
}
// compute 'prototype' response, removing minima, and add correction factor
for (i=0; i<h_len; i++) {
// compute response necessary to yeild prototype response (not exact, but close)
H_hat[i] = crealf(H_prime[i] - H_prime_min + delta) / crealf(H_tx[i] - H_tx_min + delta);
// include additional term to add stop-band suppression
H_hat[i] *= crealf(G_prime[i] - G_prime_min) / crealf(G_prime[0]);
}
// compute ifft and copy response
fft_run(h_len, H_hat, h_hat, FFT_REVERSE, 0);
for (i=0; i<h_len; i++)
hr[i] = crealf( h_hat[(i+k*m+1)%h_len] ) / (float)(k*h_len);
//
// end of filter design procedure
//
// print results to screen
printf("gmsk receive filter:\n");
for (i=0; i<h_len; i++)
printf(" hr(%3u) = %12.8f;\n", i+1, hr[i]);
// compute isi
float rxy0 = liquid_filter_crosscorr(ht,h_len, hr,h_len, 0);
float isi_rms = 0.0f;
for (i=1; i<2*m; i++) {
float e = liquid_filter_crosscorr(ht,h_len, hr,h_len, i*k) / rxy0;
isi_rms += e*e;
}
isi_rms = sqrtf(isi_rms / (float)(2*m-1));
printf("\n");
printf("ISI (RMS) = %12.8f dB\n", 20*log10f(isi_rms));
//
// export 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\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"beta = %f;\n", BT);
fprintf(fid,"h_len = 2*k*m+1;\n");
fprintf(fid,"nfft = 1024;\n");
fprintf(fid,"ht = zeros(1,h_len);\n");
fprintf(fid,"hp = zeros(1,h_len);\n");
fprintf(fid,"hr = zeros(1,h_len);\n");
// print results
for (i=0; i<h_len; i++) fprintf(fid,"ht(%3u) = %12.4e;\n", i+1, ht[i] / k);
for (i=0; i<h_len; i++) fprintf(fid,"hr(%3u) = %12.4e;\n", i+1, hr[i] * k);
for (i=0; i<h_len; i++) fprintf(fid,"hp(%3u) = %12.4e;\n", i+1, h_primef[i]);
fprintf(fid,"hc = k*conv(ht,hr);\n");
// plot results
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"Ht = 20*log10(abs(fftshift(fft(ht, nfft))));\n");
fprintf(fid,"Hp = 20*log10(abs(fftshift(fft(hp/k,nfft))));\n");
fprintf(fid,"Hr = 20*log10(abs(fftshift(fft(hr, nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc/k,nfft))));\n");
fprintf(fid,"\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Ht,'LineWidth',1,'Color',[0.00 0.25 0.50],...\n");
fprintf(fid," f,Hp,'LineWidth',1,'Color',[0.80 0.80 0.80],...\n");
fprintf(fid," f,Hr,'LineWidth',1,'Color',[0.00 0.50 0.25],...\n");
fprintf(fid," f,Hc,'LineWidth',2,'Color',[0.50 0.00 0.00],...\n");
fprintf(fid," [-0.5/k 0.5/k], [1 1]*20*log10(0.5),'or');\n");
fprintf(fid,"legend('transmit','prototype','receive','composite','alias points',1);\n");
fprintf(fid,"xlabel('Normalized Frequency');\n");
fprintf(fid,"ylabel('PSD');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([-0.5 0.5 -100 20]);\n");
fprintf(fid,"\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tr = [ -k*m:k*m]/k;\n");
fprintf(fid,"tc = [-2*k*m:2*k*m]/k;\n");
fprintf(fid,"ic = [0:k:(4*k*m)]+1;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(tr,ht,'-x', tr,hr,'-x');\n");
fprintf(fid," legend('transmit','receive',1);\n");
fprintf(fid," xlabel('Time');\n");
fprintf(fid," ylabel('GMSK Tx/Rx Filters');\n");
fprintf(fid," grid on;\n");
fprintf(fid," axis([-2*m 2*m floor(5*min([hr ht]))/5 ceil(5*max([hr ht]))/5]);\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(tc,hc,'-x', tc(ic),hc(ic),'or');\n");
fprintf(fid," xlabel('Time');\n");
fprintf(fid," ylabel('GMSK Composite Response');\n");
fprintf(fid," grid on;\n");
fprintf(fid," axis([-2*m 2*m -0.2 1.2]);\n");
fprintf(fid," axis([-2*m 2*m floor(5*min(hc))/5 ceil(5*max(hc))/5]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
return 0;
}
int main(int argc, char*argv[]) {
// options
unsigned int k=2; // samples/symbol
unsigned int m=3; // symbol delay
float beta=0.7f; // excess bandwidth factor
unsigned int num_symbols=16;
int ftype_tx = LIQUID_FIRFILT_RRC;
int ftype_rx = LIQUID_FIRFILT_RRC;
int dopt;
while ((dopt = getopt(argc,argv,"uht:k:m:b:n:")) != EOF) {
switch (dopt) {
case 'u':
case 'h':
usage();
return 0;
case 't':
if (strcmp(optarg,"gmsk")==0) {
ftype_tx = LIQUID_FIRFILT_GMSKTX;
ftype_rx = LIQUID_FIRFILT_GMSKRX;
} else {
ftype_tx = liquid_getopt_str2firfilt(optarg);
ftype_rx = liquid_getopt_str2firfilt(optarg);
}
if (ftype_tx == LIQUID_FIRFILT_UNKNOWN) {
fprintf(stderr,"error: %s, unknown filter type '%s'\n", argv[0], optarg);
exit(1);
}
break;
case 'k':
k = atoi(optarg);
break;
case 'm':
m = atoi(optarg);
break;
case 'b':
beta = atof(optarg);
break;
case 'n':
num_symbols = atoi(optarg);
break;
default:
exit(1);
}
}
if (k < 2) {
fprintf(stderr,"error: %s, k must be at least 2\n", argv[0]);
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: %s, m must be at least 1\n", argv[0]);
exit(1);
} else if (beta <= 0.0f || beta >= 1.0f) {
fprintf(stderr,"error: %s, beta must be in (0,1)\n", argv[0]);
exit(1);
}
unsigned int i;
// derived values
unsigned int num_samples = num_symbols*k;
unsigned int h_len = 2*k*m+1; // transmit/receive filter length
unsigned int hc_len = 4*k*m+1; // composite filter length
// arrays
float ht[h_len]; // transmit filter
float hr[h_len]; // receive filter
float hc[hc_len]; // composite filter
// design the filter(s)
liquid_firdes_rnyquist(ftype_tx, k, m, beta, 0, ht);
liquid_firdes_rnyquist(ftype_rx, k, m, beta, 0, hr);
for (i=0; i<h_len; i++) printf("ht(%3u) = %12.8f;\n", i+1, ht[i]);
for (i=0; i<h_len; i++) printf("hr(%3u) = %12.8f;\n", i+1, hr[i]);
#if 0
// generate receive filter coefficients (reverse of transmit)
float hr[h_len];
for (i=0; i<h_len; i++)
hr[i] = ht[h_len-i-1];
#endif
// compute composite filter response
for (i=0; i<4*k*m+1; i++) {
int lag = (int)i - (int)(2*k*m);
hc[i] = liquid_filter_crosscorr(ht,h_len, hr,h_len, lag);
}
// compute filter inter-symbol interference
float rxy0 = liquid_filter_crosscorr(ht,h_len, hr,h_len, 0);
float isi_rms=0;
for (i=1; i<2*m; i++) {
float e = liquid_filter_crosscorr(ht,h_len, hr,h_len, i*k) / rxy0;
isi_rms += e*e;
}
isi_rms = sqrtf( isi_rms / (float)(2*m-1) );
printf(" isi (rms) : %12.8f dB\n", 20*log10f(isi_rms));
// compute relative stop-band energy
unsigned int nfft = 2048;
float As = liquid_filter_energy(ht, h_len, 0.5f*(1.0f + beta)/(float)k, nfft);
printf(" As : %12.8f dB\n", 20*log10f(As));
// generate signal
float sym_in[num_symbols];
float y[num_samples];
float sym_out[num_symbols];
// create interpolator and decimator
firinterp_rrrf interp = firinterp_rrrf_create(k, ht, h_len);
firdecim_rrrf decim = firdecim_rrrf_create( k, hr, h_len);
for (i=0; i<num_symbols; i++) {
// generate random symbol
sym_in[i] = (rand() % 2) ? 1.0f : -1.0f;
// interpolate
firinterp_rrrf_execute(interp, sym_in[i], &y[i*k]);
// decimate
firdecim_rrrf_execute(decim, &y[i*k], &sym_out[i]);
// normalize output
sym_out[i] /= k;
printf(" %3u : %8.5f", i, sym_out[i]);
if (i>=2*m) printf(" *\n");
else printf("\n");
}
// clean up objects
firinterp_rrrf_destroy(interp);
firdecim_rrrf_destroy(decim);
//
// export results
//
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"beta = %12.8f;\n", beta);
fprintf(fid,"num_symbols = %u;\n", num_symbols);
fprintf(fid,"num_samples = k*num_symbols;\n");
fprintf(fid,"y = zeros(1,num_samples);\n");
for (i=0; i<num_samples; i++)
fprintf(fid," y(%3u) = %12.8f;\n", i+1, y[i]);
for (i=0; i<h_len; i++) fprintf(fid,"ht(%3u) = %20.8e;\n", i+1, ht[i]);
for (i=0; i<h_len; i++) fprintf(fid,"hr(%3u) = %20.8e;\n", i+1, hr[i]);
for (i=0; i<hc_len; i++) fprintf(fid,"hc(%3u) = %20.8e;\n", i+1, hc[i]);
fprintf(fid,"nfft=1024;\n");
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"Ht = 20*log10(abs(fftshift(fft(ht/k, nfft))));\n");
fprintf(fid,"Hr = 20*log10(abs(fftshift(fft(hr/k, nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc/k^2, nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Hc,'-','LineWidth',2,...\n");
fprintf(fid," [0.5/k],[-6],'or',...\n");
fprintf(fid," [0.5/k*(1-beta) 0.5/k*(1-beta)],[-100 10],'-r',...\n");
fprintf(fid," [0.5/k*(1+beta) 0.5/k*(1+beta)],[-100 10],'-r');\n");
fprintf(fid,"xlabel('normalized frequency');\n");
fprintf(fid,"ylabel('PSD');\n");
fprintf(fid,"axis([-0.5 0.5 -100 10]);\n");
fprintf(fid,"grid on;\n");
// compute composite filter
fprintf(fid,"figure;\n");
fprintf(fid,"hc = conv(ht,hr)/k;\n");
fprintf(fid,"t = [(-2*k*m):(2*k*m)]/k;\n");
fprintf(fid,"i0 = [0:k:4*k*m]+1;\n");
fprintf(fid,"plot(t, hc, '-s',...\n");
fprintf(fid," t(i0),hc(i0),'or');\n");
fprintf(fid,"xlabel('symbol index');\n");
fprintf(fid,"ylabel('matched filter response');\n");
fprintf(fid,"grid on;\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
