int main(int argc, char*argv[]) {
srand(time(NULL));
// options
unsigned int k = 2; // samples/symbol (input)
unsigned int k_out = 2; // samples/symbol (output)
unsigned int m = 5; // filter delay (symbols)
float beta = 0.5f; // filter excess bandwidth factor
unsigned int num_filters = 32; // number of filters in the bank
unsigned int num_symbols = 400; // number of data symbols
float SNRdB = 30.0f; // signal-to-noise ratio
// transmit/receive filter types
liquid_firfilt_type ftype_tx = LIQUID_FIRFILT_RRC;
liquid_firfilt_type ftype_rx = LIQUID_FIRFILT_RRC;
float bt = 0.02f; // loop filter bandwidth
float tau = -0.2f; // fractional symbol offset
float r = 1.00f; // resampled rate
// use random data or 101010 phasing pattern
int random_data=1;
int dopt;
while ((dopt = getopt(argc,argv,"hT:k:K:m:b:B:s:w:n:t:r:")) != EOF) {
switch (dopt) {
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 'K': k_out = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'B': num_filters = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'w': bt = atof(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
case 't': tau = atof(optarg); break;
case 'r': r = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: k (samples/symbol) must be at least 2\n");
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: m (filter delay) must be greater than 0\n");
exit(1);
} else if (beta <= 0.0f || beta > 1.0f) {
fprintf(stderr,"error: beta (excess bandwidth factor) must be in (0,1]\n");
exit(1);
} else if (num_filters == 0) {
fprintf(stderr,"error: number of polyphase filters must be greater than 0\n");
exit(1);
} else if (bt <= 0.0f) {
fprintf(stderr,"error: timing PLL bandwidth must be greater than 0\n");
exit(1);
} else if (num_symbols == 0) {
fprintf(stderr,"error: number of symbols must be greater than 0\n");
exit(1);
} else if (tau < -1.0f || tau > 1.0f) {
fprintf(stderr,"error: timing phase offset must be in [-1,1]\n");
exit(1);
} else if (r < 0.5f || r > 2.0f) {
fprintf(stderr,"error: timing frequency offset must be in [0.5,2]\n");
exit(1);
}
// compute delay
while (tau < 0) tau += 1.0f; // ensure positive tau
float g = k*tau; // number of samples offset
int ds=floorf(g); // additional symbol delay
float dt = (g - (float)ds); // fractional sample offset
if (dt > 0.5f) { // force dt to be in [0.5,0.5]
dt -= 1.0f;
ds++;
}
unsigned int i, n=0;
unsigned int num_samples = k*num_symbols;
unsigned int num_samples_resamp = (unsigned int) ceilf(num_samples*r*1.1f) + 4;
float complex s[num_symbols]; // data symbols
float complex x[num_samples]; // interpolated samples
float complex y[num_samples_resamp]; // resampled data (resamp_crcf)
float complex z[k_out*num_symbols + 64];// synchronized samples
float complex sym_out[num_symbols + 64];// synchronized symbols
for (i=0; i<num_symbols; i++) {
if (random_data) {
// random signal (QPSK)
s[i] = cexpf(_Complex_I*0.5f*M_PI*((rand() % 4) + 0.5f));
} else {
s[i] = (i%2) ? 1.0f : -1.0f; // 101010 phasing pattern
}
}
//
// create and run interpolator
//
// design interpolating filter
unsigned int h_len = 2*k*m+1;
float h[h_len];
liquid_firdes_rnyquist(ftype_tx,k,m,beta,dt,h);
firinterp_crcf q = firinterp_crcf_create(k,h,h_len);
for (i=0; i<num_symbols; i++) {
firinterp_crcf_execute(q, s[i], &x[n]);
n+=k;
}
assert(n == num_samples);
firinterp_crcf_destroy(q);
//
// run resampler
//
unsigned int resamp_len = 10*k; // resampling filter semi-length (filter delay)
float resamp_bw = 0.45f; // resampling filter bandwidth
float resamp_As = 60.0f; // resampling filter stop-band attenuation
unsigned int resamp_npfb = 64; // number of filters in bank
resamp_crcf f = resamp_crcf_create(r, resamp_len, resamp_bw, resamp_As, resamp_npfb);
unsigned int num_samples_resampled = 0;
unsigned int num_written;
for (i=0; i<num_samples; i++) {
#if 0
// bypass arbitrary resampler
y[i] = x[i];
num_samples_resampled = num_samples;
#else
// TODO : compensate for resampler filter delay
resamp_crcf_execute(f, x[i], &y[num_samples_resampled], &num_written);
num_samples_resampled += num_written;
#endif
}
resamp_crcf_destroy(f);
//
// add noise
//
float nstd = powf(10.0f, -SNRdB/20.0f);
for (i=0; i<num_samples_resampled; i++)
y[i] += nstd*(randnf() + _Complex_I*randnf());
//
// create and run symbol synchronizer
//
symsync_crcf d = symsync_crcf_create_rnyquist(ftype_rx, k, m, beta, num_filters);
symsync_crcf_set_lf_bw(d,bt);
symsync_crcf_set_output_rate(d,k_out);
unsigned int num_samples_sync=0;
unsigned int nn;
unsigned int num_symbols_sync = 0;
float tau_hat[num_samples];
for (i=ds; i<num_samples_resampled; i++) {
tau_hat[num_samples_sync] = symsync_crcf_get_tau(d);
symsync_crcf_execute(d, &y[i], 1, &z[num_samples_sync], &nn);
// decimate
unsigned int j;
for (j=0; j<nn; j++) {
if ( (num_samples_sync%k_out)==0 )
sym_out[num_symbols_sync++] = z[num_samples_sync];
num_samples_sync++;
}
}
symsync_crcf_destroy(d);
// print last several symbols to screen
printf("output symbols:\n");
printf(" ...\n");
for (i=num_symbols_sync-10; i<num_symbols_sync; i++)
printf(" sym_out(%2u) = %8.4f + j*%8.4f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[i]));
//
// export output file
//
FILE* fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s, auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"close all;\nclear all;\n\n");
fprintf(fid,"k=%u;\n",k);
fprintf(fid,"m=%u;\n",m);
fprintf(fid,"beta=%12.8f;\n",beta);
fprintf(fid,"k_out=%u;\n",k_out);
fprintf(fid,"num_filters=%u;\n",num_filters);
fprintf(fid,"num_symbols=%u;\n",num_symbols);
for (i=0; i<h_len; i++)
fprintf(fid,"h(%3u) = %12.5f;\n", i+1, h[i]);
for (i=0; i<num_symbols; i++)
fprintf(fid,"s(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(s[i]), cimagf(s[i]));
for (i=0; i<num_samples; i++)
fprintf(fid,"x(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(x[i]), cimagf(x[i]));
for (i=0; i<num_samples_resampled; i++)
fprintf(fid,"y(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
for (i=0; i<num_samples_sync; i++)
fprintf(fid,"z(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(z[i]), cimagf(z[i]));
for (i=0; i<num_symbols_sync; i++)
fprintf(fid,"sym_out(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[i]));
for (i=0; i<num_samples_sync; i++)
fprintf(fid,"tau_hat(%3u) = %12.8f;\n", i+1, tau_hat[i]);
fprintf(fid,"\n\n");
fprintf(fid,"%% scale QPSK in-phase by sqrt(2)\n");
fprintf(fid,"z = z*sqrt(2);\n");
fprintf(fid,"\n\n");
fprintf(fid,"tz = [0:length(z)-1]/k_out;\n");
fprintf(fid,"iz = 1:k_out:length(z);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(tz, real(z), '-',...\n");
fprintf(fid," tz(iz), real(z(iz)),'or');\n");
fprintf(fid,"xlabel('Time');\n");
fprintf(fid,"ylabel('Output Signal (real)');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('output time series','optimum timing','location','northeast');\n");
fprintf(fid,"iz0 = iz( 1:round(length(iz)*0.5) );\n");
fprintf(fid,"iz1 = iz( round(length(iz)*0.5):length(iz) );\n");
fprintf(fid,"figure;\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"plot(real(z(iz0)),imag(z(iz0)),'x','MarkerSize',4,'Color',[0.6 0.6 0.6]);\n");
fprintf(fid,"plot(real(z(iz1)),imag(z(iz1)),'o','MarkerSize',4,'Color',[0 0.25 0.5]);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"axis square;\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([-1 1 -1 1]*2.0);\n");
fprintf(fid,"xlabel('In-phase');\n");
fprintf(fid,"ylabel('Quadrature');\n");
fprintf(fid,"legend(['first 50%%'],['last 50%%'],'location','northeast');\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tt = 0:(length(tau_hat)-1);\n");
fprintf(fid,"b = floor(num_filters*tau_hat + 0.5);\n");
fprintf(fid,"stairs(tt,tau_hat*num_filters);\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"plot(tt,b,'-k','Color',[0 0 0]);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"xlabel('time');\n");
fprintf(fid,"ylabel('filterbank index');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([0 length(tau_hat) -1 num_filters]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
// clean it up
printf("done.\n");
return 0;
}
int main(int argc, char*argv[])
{
// options
float r = 1.1f; // resampling rate (output/input)
unsigned int m = 13; // resampling filter semi-length (filter delay)
float As = 60.0f; // resampling filter stop-band attenuation [dB]
float bw = 0.45f; // resampling filter bandwidth
unsigned int npfb = 64; // number of filters in bank (timing resolution)
unsigned int n = 400; // number of input samples
float fc = 0.044f; // complex sinusoid frequency
int dopt;
while ((dopt = getopt(argc,argv,"hr:m:b:s:p:n:f:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'r': r = atof(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': bw = atof(optarg); break;
case 's': As = atof(optarg); break;
case 'p': npfb = atoi(optarg); break;
case 'n': n = atoi(optarg); break;
case 'f': fc = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (r <= 0.0f) {
fprintf(stderr,"error: %s, resampling rate must be greater than zero\n", argv[0]);
exit(1);
} else if (m == 0) {
fprintf(stderr,"error: %s, filter semi-length must be greater than zero\n", argv[0]);
exit(1);
} else if (bw == 0.0f || bw >= 0.5f) {
fprintf(stderr,"error: %s, filter bandwidth must be in (0,0.5)\n", argv[0]);
exit(1);
} else if (As < 0.0f) {
fprintf(stderr,"error: %s, filter stop-band attenuation must be greater than zero\n", argv[0]);
exit(1);
} else if (npfb == 0) {
fprintf(stderr,"error: %s, filter bank size must be greater than zero\n", argv[0]);
exit(1);
} else if (n == 0) {
fprintf(stderr,"error: %s, number of input samples must be greater than zero\n", argv[0]);
exit(1);
}
unsigned int i;
// number of input samples (zero-padded)
unsigned int nx = n + m;
// output buffer with extra padding for good measure
unsigned int y_len = (unsigned int) ceilf(1.1 * nx * r) + 4;
// arrays
float complex x[nx];
float complex y[y_len];
// create resampler
resamp_crcf q = resamp_crcf_create(r,m,bw,As,npfb);
// generate input signal
float wsum = 0.0f;
for (i=0; i<nx; i++) {
// compute window
float w = i < n ? kaiser(i, n, 10.0f, 0.0f) : 0.0f;
// apply window to complex sinusoid
x[i] = cexpf(_Complex_I*2*M_PI*fc*i) * w;
// accumulate window
wsum += w;
}
// resample
unsigned int ny=0;
#if 0
// execute one sample at a time
unsigned int nw;
for (i=0; i<nx; i++) {
// execute resampler, storing in output buffer
resamp_crcf_execute(q, x[i], &y[ny], &nw);
// increment output size
ny += nw;
}
#else
// execute on block of samples
resamp_crcf_execute_block(q, x, nx, y, &ny);
#endif
// clean up allocated objects
resamp_crcf_destroy(q);
//
// analyze resulting signal
//
// check that the actual resampling rate is close to the target
float r_actual = (float)ny / (float)nx;
float fy = fc / r; // expected output frequency
// run FFT and ensure that carrier has moved and that image
// frequencies and distortion have been adequately suppressed
unsigned int nfft = 1 << liquid_nextpow2(ny);
float complex yfft[nfft]; // fft input
float complex Yfft[nfft]; // fft output
for (i=0; i<nfft; i++)
yfft[i] = i < ny ? y[i] : 0.0f;
fft_run(nfft, yfft, Yfft, LIQUID_FFT_FORWARD, 0);
fft_shift(Yfft, nfft); // run FFT shift
// find peak frequency
float Ypeak = 0.0f;
float fpeak = 0.0f;
float max_sidelobe = -1e9f; // maximum side-lobe [dB]
float main_lobe_width = 0.07f; // TODO: figure this out from Kaiser's equations
for (i=0; i<nfft; i++) {
// normalized output frequency
float f = (float)i/(float)nfft - 0.5f;
// scale FFT output appropriately
float Ymag = 20*log10f( cabsf(Yfft[i] / (r * wsum)) );
// find frequency location of maximum magnitude
if (Ymag > Ypeak || i==0) {
Ypeak = Ymag;
fpeak = f;
}
// find peak side-lobe value, ignoring frequencies
// within a certain range of signal frequency
if ( fabsf(f-fy) > main_lobe_width )
max_sidelobe = Ymag > max_sidelobe ? Ymag : max_sidelobe;
}
// print results and check frequency location
printf(" desired resampling rate : %12.8f\n", r);
printf(" measured resampling rate : %12.8f (%u/%u)\n", r_actual, ny, nx);
printf(" peak spectrum : %12.8f dB (expected 0.0 dB)\n", Ypeak);
printf(" peak frequency : %12.8f (expected %-12.8f)\n", fpeak, fy);
printf(" max sidelobe : %12.8f dB (expected at least %.2f dB)\n", max_sidelobe, -As);
//
// export results
//
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,"m=%u;\n", m);
fprintf(fid,"npfb=%u;\n", npfb);
fprintf(fid,"r=%12.8f;\n", r);
fprintf(fid,"nx = %u;\n", nx);
fprintf(fid,"x = zeros(1,nx);\n");
for (i=0; i<nx; i++)
fprintf(fid,"x(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"ny = %u;\n", ny);
fprintf(fid,"y = zeros(1,ny);\n");
for (i=0; i<ny; i++)
fprintf(fid,"y(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"\n\n");
fprintf(fid,"%% plot frequency-domain result\n");
fprintf(fid,"nfft=2^nextpow2(max(nx,ny));\n");
fprintf(fid,"%% estimate PSD, normalize by array length\n");
fprintf(fid,"X=20*log10(abs(fftshift(fft(x,nfft)/length(x))));\n");
fprintf(fid,"Y=20*log10(abs(fftshift(fft(y,nfft)/length(y))));\n");
fprintf(fid,"G=max(X);\n");
fprintf(fid,"X=X-G;\n");
fprintf(fid,"Y=Y-G;\n");
fprintf(fid,"f=[0:(nfft-1)]/nfft-0.5;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"if r>1, fx = f/r; fy = f; %% interpolated\n");
fprintf(fid,"else, fx = f; fy = f*r; %% decimated\n");
fprintf(fid,"end;\n");
fprintf(fid,"plot(fx,X,'Color',[0.5 0.5 0.5],fy,Y,'LineWidth',2);\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"xlabel('normalized frequency');\n");
fprintf(fid,"ylabel('PSD [dB]');\n");
fprintf(fid,"legend('original','resampled','location','northeast');");
fprintf(fid,"axis([-0.5 0.5 -120 20]);\n");
fprintf(fid,"\n\n");
fprintf(fid,"%% plot time-domain result\n");
fprintf(fid,"tx=[0:(length(x)-1)];\n");
fprintf(fid,"ty=[0:(length(y)-1)]/r-m;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(tx,real(x),'-s','Color',[0.5 0.5 0.5],'MarkerSize',1,...\n");
fprintf(fid," ty,real(y),'-s','Color',[0.5 0 0], 'MarkerSize',1);\n");
fprintf(fid," legend('original','resampled','location','northeast');");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('real');\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(tx,imag(x),'-s','Color',[0.5 0.5 0.5],'MarkerSize',1,...\n");
fprintf(fid," ty,imag(y),'-s','Color',[0 0.5 0], 'MarkerSize',1);\n");
fprintf(fid," legend('original','resampled','location','northeast');");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('imag');\n");
fclose(fid);
printf("results written to %s\n",OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
int main() {
// options
unsigned int h_len = 7; // filter semi-length (filter delay)
float r=1/sqrtf(2); // resampling rate (output/input)
float bw=0.25f; // resampling filter bandwidth
float As=60.0f; // resampling filter stop-band attenuation [dB]
unsigned int npfb=32; // number of filters in bank (timing resolution)
unsigned int n=180; // number of input samples
// number of input samples (adjusted for filter delay)
unsigned int nx = n + h_len;
// generate input sequence : windowed sum of complex sinusoids
unsigned int i;
float complex x[nx];
for (i=0; i<nx; i++) {
float complex jphi = _Complex_I*2.0f*M_PI*i;
x[i] = cexpf(jphi*0.02f) + 1.4f*cexpf(jphi*0.07f);
// window edge size
unsigned int t = (unsigned int)(0.1*n);
if (i < n) {
// edge-rounded window
if (i < t) x[i] *= blackmanharris(i,2*t);
else if (i >= n-t) x[i] *= blackmanharris(n-i-1,2*t);
} else {
x[i] = 0.;
}
}
// output buffer with extra padding for good measure
unsigned int y_len = (unsigned int) ceilf(1.1*r*nx) + 16;
float complex y[y_len];
// create resampler
resamp_crcf f = resamp_crcf_create(r,h_len,bw,As,npfb);
unsigned int num_written;
unsigned int ny=0;
for (i=0; i<nx; i++) {
// execute resampler, storing in output buffer
resamp_crcf_execute(f, x[i], &y[ny], &num_written);
ny += num_written;
}
printf(" %u / %u\n", ny, nx);
// clean up allocated objects
resamp_crcf_destroy(f);
// open/initialize output file
FILE*fid = fopen(OUTPUT_FILENAME_TIME,"w");
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME_TIME);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
//fprintf(fid,"set xrange [0:%u];\n",n);
fprintf(fid,"set yrange [-3:3]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Input Sample Index'\n");
fprintf(fid,"set key top right nobox\n");
fprintf(fid,"set ytics -5,1,5\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set pointsize 0.6\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n", LIQUID_DOC_COLOR_GRID);
fprintf(fid,"set multiplot layout 2,1 scale 1.0,1.0\n");
fprintf(fid,"# real\n");
fprintf(fid,"set ylabel 'Real'\n");
fprintf(fid,"plot '-' using 1:2 with linespoints pointtype 7 linetype 1 linewidth 1 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '#008000' title 'resampled'\n");
// export output
for (i=0; i<nx; i++) {
//fprintf(fid,"%6u %12.4e %12.4e\n", i, cos(2*M_PI*0.04*i), sin(2*M_PI*0.04*i));
fprintf(fid,"%6u %12.4e %12.4e\n", i, crealf(x[i]), cimagf(x[i]));
}
fprintf(fid,"e\n");
float t;
for (i=0; i<ny; i++) {
t = (float)(i) / r - (float)(h_len);
fprintf(fid,"%12.4e %12.4e %12.4e\n", t, crealf(y[i]), cimagf(y[i]));
}
fprintf(fid,"e\n");
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:3 with linespoints pointtype 7 linetype 1 linewidth 1 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:3 with points pointtype 7 linecolor rgb '#800000' title 'resampled'\n");
// export output
for (i=0; i<nx; i++) {
//fprintf(fid,"%6u %12.4e %12.4e\n", i, cos(2*M_PI*0.04*i), sin(2*M_PI*0.04*i));
fprintf(fid,"%6u %12.4e %12.4e\n", i, crealf(x[i]), cimagf(x[i]));
}
fprintf(fid,"e\n");
for (i=0; i<ny; i++) {
t = (float)(i) / r - (float)(h_len);
fprintf(fid,"%12.4e %12.4e %12.4e\n", t, crealf(y[i]), cimagf(y[i]));
}
fprintf(fid,"e\n");
fprintf(fid,"unset multiplot\n");
// close output file
fclose(fid);
fid = fopen(OUTPUT_FILENAME_FREQ,"w");
unsigned int nfft = 512;
float complex X[nfft];
float complex Y[nfft];
liquid_doc_compute_psdcf(x,nx,X,nfft,LIQUID_DOC_PSDWINDOW_HANN,0);
liquid_doc_compute_psdcf(y,ny,Y,nfft,LIQUID_DOC_PSDWINDOW_HANN,0);
fft_shift(X,nfft);
fft_shift(Y,nfft);
float scaling_factor = 20*log10f(nfft);
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME_FREQ);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set xrange [-0.5:0.5];\n");
fprintf(fid,"set yrange [-120:20]\n");
fprintf(fid,"set size ratio 0.6\n");
fprintf(fid,"set xlabel 'Normalized Input Frequency'\n");
fprintf(fid,"set ylabel 'Power Spectral Density [dB]'\n");
fprintf(fid,"set key top right nobox\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set pointsize 0.6\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"# real\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 4 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 4 linecolor rgb '#004080' title 'resampled'\n");
// export output
for (i=0; i<nfft; i++) {
float fx = (float)(i) / (float)nfft - 0.5f;
fprintf(fid,"%12.8f %12.4e\n", fx, 20*log10f(cabsf(X[i])) - scaling_factor);
}
fprintf(fid,"e\n");
for (i=0; i<nfft; i++) {
float fy = ((float)(i) / (float)nfft - 0.5f)*r;
fprintf(fid,"%12.8f %12.4e\n", fy, 20*log10f(cabsf(Y[i])) - scaling_factor - 20*log10(r));
}
fprintf(fid,"e\n");
fclose(fid);
printf("done.\n");
return 0;
}
int main(int argc, char*argv[]) {
srand(time(NULL));
// options
unsigned int k=2; // samples/symbol
unsigned int m=3; // filter delay (symbols)
float beta=0.9f; // filter excess bandwidth factor
unsigned int order=2;
unsigned int num_symbols=1024;
float SNRdB = 30.0f;
float bt=0.02f; // loop filter bandwidth
float tau=0.2f; // fractional symbol offset
float r = 1.00f; // resampled rate
// use random data or 101010 phasing pattern
int random_data=1;
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:o:s:w:n:t:r:")) != 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;
case 'o': order = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'w': bt = atof(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
case 't': tau = atof(optarg); break;
case 'r': r = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: k (samples/symbol) must be at least 2\n");
return 1;
} else if (m < 1) {
fprintf(stderr,"error: m (filter delay) must be greater than 0\n");
return 1;
} else if (beta <= 0.0f || beta > 1.0f) {
fprintf(stderr,"error: beta (excess bandwidth factor) must be in (0,1]\n");
return 1;
} else if (order == 0) {
fprintf(stderr,"error: number of polyphase filters must be greater than 0\n");
return 1;
} else if (bt <= 0.0f) {
fprintf(stderr,"error: timing PLL bandwidth must be greater than 0\n");
return 1;
} else if (num_symbols == 0) {
fprintf(stderr,"error: number of symbols must be greater than 0\n");
return 1;
} else if (tau < -1.0f || tau > 1.0f) {
fprintf(stderr,"error: timing phase offset must be in [-1,1]\n");
return 1;
} else if (r < 0.5f || r > 2.0f) {
fprintf(stderr,"error: timing frequency offset must be in [0.5,2]\n");
return 1;
}
// compute delay
while (tau < 0) tau += 1.0f; // ensure positive tau
float g = k*tau; // number of samples offset
int ds=floorf(g); // additional symbol delay
float dt = (g - (float)ds); // fractional sample offset
unsigned int i, n=0;
unsigned int num_samples = k*num_symbols;
unsigned int num_samples_resamp = (unsigned int) ceilf(num_samples*r*1.1f) + 4;
float complex s[num_symbols]; // data symbols
float complex x[num_samples]; // interpolated samples
float complex y[num_samples_resamp]; // resampled data (resamp_crcf)
float complex z[num_symbols + 64]; // synchronized symbols
for (i=0; i<num_symbols; i++) {
if (random_data) {
// random signal (QPSK)
s[i] = cexpf(_Complex_I*0.5f*M_PI*((rand() % 4) + 0.5f));
} else {
s[i] = (i%2) ? 1.0f : -1.0f; // 101010 phasing pattern
}
}
//
// create and run interpolator
//
// design interpolating filter
unsigned int h_len = 2*k*m + 1;
float h[h_len];
liquid_firdes_rcos(k,m,beta,dt,h);
interp_crcf q = interp_crcf_create(k,h,h_len);
for (i=0; i<num_symbols; i++) {
interp_crcf_execute(q, s[i], &x[n]);
n+=k;
}
assert(n == num_samples);
interp_crcf_destroy(q);
//
// run resampler
//
unsigned int resamp_len = 10*k; // resampling filter semi-length (filter delay)
float resamp_bw = 0.45f; // resampling filter bandwidth
float resamp_As = 60.0f; // resampling filter stop-band attenuation
unsigned int resamp_npfb = 64; // number of filters in bank
resamp_crcf f = resamp_crcf_create(r, resamp_len, resamp_bw, resamp_As, resamp_npfb);
unsigned int num_samples_resampled = 0;
unsigned int num_written;
for (i=0; i<num_samples; i++) {
#if 0
// bypass arbitrary resampler
y[i] = x[i];
num_samples_resampled = num_samples;
#else
// TODO : compensate for resampler filter delay
resamp_crcf_execute(f, x[i], &y[num_samples_resampled], &num_written);
num_samples_resampled += num_written;
#endif
}
resamp_crcf_destroy(f);
//
// add noise
//
float nstd = powf(10.0f, -SNRdB/20.0f) / sqrtf(2.0f);
for (i=0; i<num_samples_resampled; i++)
y[i] += nstd*(randnf() + _Complex_I*randnf());
//
// create and run symbol synchronizer
//
// create symbol synchronizer
symsynclp_crcf d = symsynclp_crcf_create(k, order);
symsynclp_crcf_set_lf_bw(d,bt);
unsigned int num_symbols_sync=0;
unsigned int nn;
float tau_hat[num_samples];
for (i=ds; i<num_samples_resampled; i++) {
tau_hat[num_symbols_sync] = symsynclp_crcf_get_tau(d);
symsynclp_crcf_execute(d, &y[i], 1, &z[num_symbols_sync], &nn);
num_symbols_sync += nn;
}
symsynclp_crcf_destroy(d);
// print last several symbols to screen
printf("z(t) :\n");
for (i=num_symbols_sync-10; i<num_symbols_sync; i++)
printf(" z(%2u) = %8.4f + j*%8.4f;\n", i+1, crealf(z[i]), cimagf(z[i]));
//
// export output file
//
FILE* fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s, auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"close all;\nclear all;\n\n");
fprintf(fid,"k=%u;\n",k);
fprintf(fid,"m=%u;\n",m);
fprintf(fid,"beta=%12.8f;\n",beta);
fprintf(fid,"order=%u;\n",order);
fprintf(fid,"num_symbols=%u;\n",num_symbols);
for (i=0; i<h_len; i++)
fprintf(fid,"h(%3u) = %12.5f;\n", i+1, h[i]);
for (i=0; i<num_symbols; i++)
fprintf(fid,"s(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(s[i]), cimagf(s[i]));
for (i=0; i<num_samples; i++)
fprintf(fid,"x(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(x[i]), cimagf(x[i]));
for (i=0; i<num_samples_resampled; i++)
fprintf(fid,"y(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
for (i=0; i<num_symbols_sync; i++)
fprintf(fid,"z(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(z[i]), cimagf(z[i]));
for (i=0; i<num_symbols_sync; i++)
fprintf(fid,"tau_hat(%3u) = %12.8f;\n", i+1, tau_hat[i]);
fprintf(fid,"\n\n");
fprintf(fid,"ms = 8; %% marker size\n");
fprintf(fid,"zp = filter(h,1,y);\n");
fprintf(fid,"figure;\nhold on;\n");
fprintf(fid,"plot([0:length(s)-1], real(s), 'ob', 'MarkerSize',ms);\n");
fprintf(fid,"plot([0:length(y)-1]/k -m, real(y), '-', 'MarkerSize',ms, 'Color',[0.8 0.8 0.8]);\n");
fprintf(fid,"plot([0:length(zp)-1]/k -k*m, real(zp/k), '-b', 'MarkerSize',ms);\n");
fprintf(fid,"plot([0:length(z)-1] -k*m+1,real(z), 'xr', 'MarkerSize',ms);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"xlabel('Symbol Index');\n");
fprintf(fid,"ylabel('Output Signal');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('sym in','interp','mf','sym out',0);\n");
fprintf(fid,"t0=1:floor(0.25*length(z));\n");
fprintf(fid,"t1=ceil(0.25*length(z)):length(z);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"plot(real(z(t0)),imag(z(t0)),'x','MarkerSize',ms,'Color',[0.6 0.6 0.6]);\n");
fprintf(fid,"plot(real(z(t1)),imag(z(t1)),'x','MarkerSize',ms,'Color',[0 0.25 0.5]);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"axis square; grid on;\n");
fprintf(fid,"axis([-1 1 -1 1]*1.2);\n");
fprintf(fid,"xlabel('In-phase');\n");
fprintf(fid,"ylabel('Quadrature');\n");
fprintf(fid,"legend(['first 25%%'],['last 75%%'],1);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tt = 0:(length(tau_hat)-1);\n");
fprintf(fid,"plot(tt,tau_hat,'-k','Color',[0 0 0]);\n");
fprintf(fid,"xlabel('time');\n");
fprintf(fid,"ylabel('tau-hat');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([0 length(tau_hat) 0 1]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
// clean it up
printf("done.\n");
return 0;
}
int main(int argc, char*argv[]) {
srand(time(NULL));
// options
unsigned int k=2; // samples/symbol (input)
unsigned int k_out=2; // samples/symbol (output)
unsigned int m=4; // filter delay (symbols)
float beta=0.3f; // filter excess bandwidth factor
unsigned int num_filters=64; // number of filters in the bank
unsigned int num_symbols=500; // number of data symbols
float SNRdB = 30.0f; // signal-to-noise ratio
liquid_rnyquist_type ftype_tx = LIQUID_RNYQUIST_RRC;
liquid_rnyquist_type ftype_rx = LIQUID_RNYQUIST_RRC;
float bt=0.01f; // loop filter bandwidth
float tau=-0.4f; // fractional symbol offset
float r = 1.00f; // resampled rate
char filename_base[256] = "figures.gen/filter_symsync_crcf";
int dopt;
while ((dopt = getopt(argc,argv,"hf:k:K:m:b:B:s:w:n:t:r:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'f': strncpy(filename_base,optarg,256); break;
case 'k': k = atoi(optarg); break;
case 'K': k_out = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'B': num_filters = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'w': bt = atof(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
case 't': tau = atof(optarg); break;
case 'r': r = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: k (samples/symbol) must be at least 2\n");
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: m (filter delay) must be greater than 0\n");
exit(1);
} else if (beta <= 0.0f || beta > 1.0f) {
fprintf(stderr,"error: beta (excess bandwidth factor) must be in (0,1]\n");
exit(1);
} else if (num_filters == 0) {
fprintf(stderr,"error: number of polyphase filters must be greater than 0\n");
exit(1);
} else if (bt <= 0.0f) {
fprintf(stderr,"error: timing PLL bandwidth must be greater than 0\n");
exit(1);
} else if (num_symbols == 0) {
fprintf(stderr,"error: number of symbols must be greater than 0\n");
exit(1);
} else if (tau < -1.0f || tau > 1.0f) {
fprintf(stderr,"error: timing phase offset must be in [-1,1]\n");
exit(1);
} else if (r < 0.5f || r > 2.0f) {
fprintf(stderr,"error: timing frequency offset must be in [0.5,2]\n");
exit(1);
}
// compute delay
while (tau < 0) tau += 1.0f; // ensure positive tau
float g = k*tau; // number of samples offset
int ds=floorf(g); // additional symbol delay
float dt = (g - (float)ds); // fractional sample offset
if (dt > 0.5f) { // force dt to be in [0.5,0.5]
dt -= 1.0f;
ds++;
}
unsigned int i, n=0;
// derived values
unsigned int num_samples = k*num_symbols;
unsigned int num_samples_resamp = (unsigned int) ceilf(num_samples*r*1.1f) + 4;
// arrays
float complex s[num_symbols]; // data symbols
float complex x[num_samples]; // interpolated samples
float complex y[num_samples_resamp]; // resampled data (resamp_crcf)
float complex z[k_out*num_symbols + 64];// synchronized samples
float complex sym_out[num_symbols + 64];// synchronized symbols
// random signal (QPSK)
for (i=0; i<num_symbols; i++) {
s[i] = ( rand() % 2 ? M_SQRT1_2 : -M_SQRT1_2 ) +
( rand() % 2 ? M_SQRT1_2 : -M_SQRT1_2 ) * _Complex_I;
}
//
// create and run interpolator
//
// design interpolating filter
unsigned int h_len = 2*k*m+1;
float h[h_len];
liquid_firdes_rnyquist(ftype_tx,k,m,beta,dt,h);
interp_crcf q = interp_crcf_create(k,h,h_len);
for (i=0; i<num_symbols; i++) {
interp_crcf_execute(q, s[i], &x[n]);
n+=k;
}
assert(n == num_samples);
interp_crcf_destroy(q);
//
// run resampler
//
unsigned int resamp_len = 10*k; // resampling filter semi-length (filter delay)
float resamp_bw = 0.45f; // resampling filter bandwidth
float resamp_As = 60.0f; // resampling filter stop-band attenuation
unsigned int resamp_npfb = 64; // number of filters in bank
resamp_crcf f = resamp_crcf_create(r, resamp_len, resamp_bw, resamp_As, resamp_npfb);
unsigned int num_samples_resampled = 0;
unsigned int num_written;
for (i=0; i<num_samples; i++) {
#if 0
// bypass arbitrary resampler
y[i] = x[i];
num_samples_resampled = num_samples;
#else
// TODO : compensate for resampler filter delay
resamp_crcf_execute(f, x[i], &y[num_samples_resampled], &num_written);
num_samples_resampled += num_written;
#endif
}
resamp_crcf_destroy(f);
//
// add noise
//
float nstd = powf(10.0f, -SNRdB/20.0f);
for (i=0; i<num_samples_resampled; i++)
y[i] += nstd*(randnf() + _Complex_I*randnf());
//
// create and run symbol synchronizer
//
symsync_crcf d = symsync_crcf_create_rnyquist(ftype_rx, k, m, beta, num_filters);
symsync_crcf_set_lf_bw(d,bt);
symsync_crcf_set_output_rate(d,k_out);
unsigned int num_samples_sync=0;
unsigned int nn;
unsigned int num_symbols_sync = 0;
float tau_hat[num_samples];
for (i=ds; i<num_samples_resampled; i++) {
tau_hat[num_samples_sync] = symsync_crcf_get_tau(d);
symsync_crcf_execute(d, &y[i], 1, &z[num_samples_sync], &nn);
// decimate
unsigned int j;
for (j=0; j<nn; j++) {
if ( (num_samples_sync%k_out)==0 )
sym_out[num_symbols_sync++] = z[num_samples_sync];
num_samples_sync++;
}
}
symsync_crcf_destroy(d);
// print last several symbols to screen
printf("output symbols:\n");
for (i=num_symbols_sync-10; i<num_symbols_sync; i++)
printf(" sym_out(%2u) = %8.4f + j*%8.4f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[i]));
//
// export output
//
FILE * fid = NULL;
char filename[300];
//
// const: constellation
//
strncpy(filename, filename_base, 256);
strcat(filename, "_const.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 1\n");
fprintf(fid,"set xrange [-1.5:1.5];\n");
fprintf(fid,"set yrange [-1.5:1.5];\n");
fprintf(fid,"set xlabel 'In-phase'\n");
fprintf(fid,"set ylabel 'Quadrature phase'\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' linewidth 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with points pointtype 7 pointsize 0.5 linecolor rgb '%s' title 'first %u symbols',\\\n", LIQUID_DOC_COLOR_GRAY, num_symbols/2);
fprintf(fid," '-' using 1:2 with points pointtype 7 pointsize 0.7 linecolor rgb '%s' title 'last %u symbols'\n", LIQUID_DOC_COLOR_RED, num_symbols/2);
// first half of symbols
for (i=2*m; i<num_symbols_sync/2; i++)
fprintf(fid," %12.4e %12.4e\n", crealf(sym_out[i]), cimagf(sym_out[i]));
fprintf(fid,"e\n");
// second half of symbols
for ( ; i<num_symbols_sync; i++)
fprintf(fid," %12.4e %12.4e\n", crealf(sym_out[i]), cimagf(sym_out[i]));
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// time series
//
strncpy(filename, filename_base, 256);
strcat(filename, "_time.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set xrange [0:%u];\n",num_symbols);
fprintf(fid,"set yrange [-1.5:1.5]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Symbol Index'\n");
fprintf(fid,"set key top right nobox\n");
//fprintf(fid,"set ytics -5,1,5\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set pointsize 0.6\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n", LIQUID_DOC_COLOR_GRID);
fprintf(fid,"set multiplot layout 2,1 scale 1.0,1.0\n");
// real
fprintf(fid,"# real\n");
fprintf(fid,"set ylabel 'Real'\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1 linecolor rgb '#999999' notitle,\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' notitle'\n", LIQUID_DOC_COLOR_BLUE);
//
for (i=0; i<num_samples_sync; i++)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k_out, crealf(z[i]));
fprintf(fid,"e\n");
//
for (i=0; i<num_samples_sync; i+=k)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k_out, crealf(z[i]));
fprintf(fid,"e\n");
// imag
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1 linecolor rgb '#999999' notitle,\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' notitle'\n", LIQUID_DOC_COLOR_GREEN);
//
for (i=0; i<num_samples_sync; i++)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k_out, cimagf(z[i]));
fprintf(fid,"e\n");
//
for (i=0; i<num_samples_sync; i+=k)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k_out, cimagf(z[i]));
fprintf(fid,"e\n");
fprintf(fid,"unset multiplot\n");
// close output file
fclose(fid);
printf("results written to '%s'\n", filename);
// clean it up
return 0;
}
