// autotest helper function
// _b : filter coefficients (numerator)
// _a : filter coefficients (denominator)
// _h_len : filter coefficients length
// _x : input array
// _x_len : input array length
// _y : output array
// _y_len : output array length
void iirfilt_rrrf_test(float * _b,
float * _a,
unsigned int _h_len,
float * _x,
unsigned int _x_len,
float * _y,
unsigned int _y_len)
{
float tol = 0.001f;
// load filter coefficients externally
iirfilt_rrrf q = iirfilt_rrrf_create(_b, _h_len, _a, _h_len);
// allocate memory for output
float y_test[_y_len];
unsigned int i;
// compute output
for (i=0; i<_x_len; i++) {
iirfilt_rrrf_execute(q, _x[i], &y_test[i]);
CONTEND_DELTA( y_test[i], _y[i], tol );
}
// destroy filter object
iirfilt_rrrf_destroy(q);
}
//
// AUTOTEST : iir group delay, n=3
//
void autotest_iir_groupdelay_n3()
{
// create coefficients array
float b[3] = {0.20657210, 0.41314420, 0.20657210};
float a[3] = {1.00000000, -0.36952737, 0.19581573};
float tol = 1e-3f;
unsigned int i;
// create testing vectors
float fc[4] = { 0.000,
0.125,
0.250,
0.375};
float g0[4] = { 0.973248939389634,
1.366481121240365,
1.227756735863196,
0.651058521306726};
// run tests
float g;
for (i=0; i<4; i++) {
g = iir_group_delay(b, 3, a, 3, fc[i]);
CONTEND_DELTA( g, g0[i], tol );
}
// create filter
iirfilt_rrrf filter = iirfilt_rrrf_create(b,3,a,3);
// run tests again
for (i=0; i<4; i++) {
g = iirfilt_rrrf_groupdelay(filter, fc[i]);
CONTEND_DELTA( g, g0[i], tol );
}
// destroy filter
iirfilt_rrrf_destroy(filter);
}
//
// AUTOTEST : iir group delay, n=8
//
void autotest_iir_groupdelay_n8()
{
// create coefficients arrays (7th-order Butterworth)
float b[8];
b[ 0] = 0.00484212;
b[ 1] = 0.03389481;
b[ 2] = 0.10168444;
b[ 3] = 0.16947407;
b[ 4] = 0.16947407;
b[ 5] = 0.10168444;
b[ 6] = 0.03389481;
b[ 7] = 0.00484212;
float a[8];
a[ 0] = 1.00000000;
a[ 1] = -1.38928008;
a[ 2] = 1.67502367;
a[ 3] = -1.05389738;
a[ 4] = 0.50855154;
a[ 5] = -0.14482945;
a[ 6] = 0.02625222;
a[ 7] = -0.00202968;
float tol = 1e-3f;
unsigned int i;
// create testing vectors
float fc[7] = { 0.00000,
0.06250,
0.12500,
0.18750,
0.25000,
0.31250,
0.37500};
float g0[7] = { 3.09280801068444,
3.30599360247944,
4.18341028373046,
7.71934054380586,
4.34330109915390,
2.60203085226210,
1.97868452107144};
// run tests
float g;
for (i=0; i<7; i++) {
g = iir_group_delay(b, 8, a, 8, fc[i]);
CONTEND_DELTA( g, g0[i], tol );
}
//
// test with iir filter (tf)
//
// create filter
iirfilt_rrrf filter = iirfilt_rrrf_create(b,8,a,8);
// run tests again
for (i=0; i<7; i++) {
g = iirfilt_rrrf_groupdelay(filter, fc[i]);
CONTEND_DELTA( g, g0[i], tol );
}
// destroy filter
iirfilt_rrrf_destroy(filter);
}
int main(int argc, char*argv[]) {
srand( time(NULL) );
// options
float phase_offset = M_PI / 4.0f; // phase offset
float frequency_offset = 0.3f; // frequency offset
float pll_bandwidth = 0.01f; // PLL bandwidth
float zeta = 1/sqrtf(2.0f); // PLL damping factor
float K = 1000.0f; // PLL loop gain
unsigned int n=512; // number of iterations
int dopt;
while ((dopt = getopt(argc,argv,"uhb:z:K:n:p:f:")) != EOF) {
switch (dopt) {
case 'u':
case 'h':
usage();
return 0;
case 'b':
pll_bandwidth = atof(optarg);
break;
case 'z':
zeta = atof(optarg);
break;
case 'K':
K = atof(optarg);
break;
case 'n':
n = atoi(optarg);
break;
case 'p':
phase_offset = atof(optarg);
break;
case 'f':
frequency_offset= atof(optarg);
break;
default:
exit(1);
}
}
unsigned int d=n/32; // print every "d" lines
// validate input
if (pll_bandwidth <= 0.0f) {
fprintf(stderr,"error: bandwidth must be greater than 0\n");
exit(1);
} else if (zeta <= 0.0f) {
fprintf(stderr,"error: damping factor must be greater than 0\n");
exit(1);
} else if (K <= 0.0f) {
fprintf(stderr,"error: loop gain must be greater than 0\n");
exit(1);
}
// data arrays
float complex x[n]; // input complex sinusoid
float complex y[n]; // output complex sinusoid
float phase_error[n]; // output phase error
// generate PLL filter
float b[3];
float a[3];
iirdes_pll_active_lag(pll_bandwidth, zeta, K, b, a);
iirfilt_rrrf pll = iirfilt_rrrf_create(b,3,a,3);
iirfilt_rrrf_print(pll);
unsigned int i;
float phi;
for (i=0; i<n; i++) {
phi = phase_offset + i*frequency_offset;
x[i] = cexpf(_Complex_I*phi);
}
// run loop
float theta = 0.0f;
y[0] = 1.0f;
for (i=0; i<n; i++) {
// generate complex sinusoid
y[i] = cexpf(_Complex_I*theta);
// compute phase error
phase_error[i] = cargf(x[i]*conjf(y[i]));
// update pll
iirfilt_rrrf_execute(pll, phase_error[i], &theta);
// print phase error
if ((i)%d == 0 || i==n-1 || i==0)
printf("%4u : phase error = %12.8f\n", i, phase_error[i]);
}
// destroy filter object
iirfilt_rrrf_destroy(pll);
// write 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", n);
fprintf(fid,"x = zeros(1,n);\n");
fprintf(fid,"y = zeros(1,n);\n");
for (i=0; i<n; i++) {
fprintf(fid,"x(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"e(%4u) = %12.4e;\n", i+1, phase_error[i]);
}
fprintf(fid,"t=0:(n-1);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(t,real(x),t,real(y));\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('real');\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(t,imag(x),t,imag(y));\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('imag');\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(t,e);\n");
fprintf(fid,"xlabel('time');\n");
fprintf(fid,"ylabel('phase error');\n");
fprintf(fid,"grid on;\n");
fclose(fid);
printf("results written to %s.\n",OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
int main(int argc, char*argv[]) {
// options
unsigned int k = 8; // filter samples/symbol
unsigned int bps= 1; // number of bits/symbol
float h = 0.5f; // modulation index (h=1/2 for MSK)
unsigned int num_data_symbols = 20; // number of data symbols
float SNRdB = 80.0f; // signal-to-noise ratio [dB]
float cfo = 0.0f; // carrier frequency offset
float cpo = 0.0f; // carrier phase offset
float tau = 0.0f; // fractional symbol offset
enum {
TXFILT_SQUARE=0,
TXFILT_RCOS_FULL,
TXFILT_RCOS_HALF,
TXFILT_GMSK,
} tx_filter_type = TXFILT_SQUARE;
float gmsk_bt = 0.35f; // GMSK bandwidth-time factor
int dopt;
while ((dopt = getopt(argc,argv,"ht:k:b:H:B:n:s:F:P:T:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 't':
if (strcmp(optarg,"square")==0) {
tx_filter_type = TXFILT_SQUARE;
} else if (strcmp(optarg,"rcos-full")==0) {
tx_filter_type = TXFILT_RCOS_FULL;
} else if (strcmp(optarg,"rcos-half")==0) {
tx_filter_type = TXFILT_RCOS_HALF;
} else if (strcmp(optarg,"gmsk")==0) {
tx_filter_type = TXFILT_GMSK;
} else {
fprintf(stderr,"error: %s, unknown filter type '%s'\n", argv[0], optarg);
exit(1);
}
break;
case 'k': k = atoi(optarg); break;
case 'b': bps = atoi(optarg); break;
case 'H': h = atof(optarg); break;
case 'B': gmsk_bt = atof(optarg); break;
case 'n': num_data_symbols = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'F': cfo = atof(optarg); break;
case 'P': cpo = atof(optarg); break;
case 'T': tau = atof(optarg); break;
default:
exit(1);
}
}
unsigned int i;
// derived values
unsigned int num_symbols = num_data_symbols;
unsigned int num_samples = k*num_symbols;
unsigned int M = 1 << bps; // constellation size
float nstd = powf(10.0f, -SNRdB/20.0f);
// arrays
unsigned char sym_in[num_symbols]; // input symbols
float phi[num_samples]; // transmitted phase
float complex x[num_samples]; // transmitted signal
float complex y[num_samples]; // received signal
float complex z[num_samples]; // output...
//unsigned char sym_out[num_symbols]; // output symbols
unsigned int ht_len = 0;
unsigned int tx_delay = 0;
float * ht = NULL;
switch (tx_filter_type) {
case TXFILT_SQUARE:
// regular MSK
ht_len = k;
tx_delay = 1;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = h * M_PI / (float)k;
break;
case TXFILT_RCOS_FULL:
// full-response raised-cosine pulse
ht_len = k;
tx_delay = 1;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = h * M_PI / (float)k * (1.0f - cosf(2.0f*M_PI*i/(float)ht_len));
break;
case TXFILT_RCOS_HALF:
// partial-response raised-cosine pulse
ht_len = 3*k;
tx_delay = 2;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = 0.0f;
for (i=0; i<2*k; i++)
ht[i+k/2] = h * 0.5f * M_PI / (float)k * (1.0f - cosf(2.0f*M_PI*i/(float)(2*k)));
break;
case TXFILT_GMSK:
ht_len = 2*k*3+1+k;
tx_delay = 4;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = 0.0f;
liquid_firdes_gmsktx(k,3,gmsk_bt,0.0f,&ht[k/2]);
for (i=0; i<ht_len; i++)
ht[i] *= h * 2.0f / (float)k;
break;
default:
fprintf(stderr,"error: %s, invalid tx filter type\n", argv[0]);
exit(1);
}
for (i=0; i<ht_len; i++)
printf("ht(%3u) = %12.8f;\n", i+1, ht[i]);
firinterp_rrrf interp_tx = firinterp_rrrf_create(k, ht, ht_len);
// generate symbols and interpolate
// phase-accumulating filter (trapezoidal integrator)
float b[2] = {0.5f, 0.5f};
if (tx_filter_type == TXFILT_SQUARE) {
// square filter: rectangular integration with one sample of delay
b[0] = 0.0f;
b[1] = 1.0f;
}
float a[2] = {1.0f, -1.0f};
iirfilt_rrrf integrator = iirfilt_rrrf_create(b,2,a,2);
float theta = 0.0f;
for (i=0; i<num_symbols; i++) {
sym_in[i] = rand() % M;
float v = 2.0f*sym_in[i] - (float)(M-1); // +/-1, +/-3, ... +/-(M-1)
firinterp_rrrf_execute(interp_tx, v, &phi[k*i]);
// accumulate phase
unsigned int j;
for (j=0; j<k; j++) {
iirfilt_rrrf_execute(integrator, phi[i*k+j], &theta);
x[i*k+j] = cexpf(_Complex_I*theta);
}
}
iirfilt_rrrf_destroy(integrator);
// push through channel
for (i=0; i<num_samples; i++) {
// add carrier frequency/phase offset
y[i] = x[i]*cexpf(_Complex_I*(cfo*i + cpo));
// add noise
y[i] += nstd*(randnf() + _Complex_I*randnf())*M_SQRT1_2;
}
// create decimator
unsigned int m = 3;
float bw = 0.0f;
float beta = 0.0f;
firfilt_crcf decim_rx = NULL;
switch (tx_filter_type) {
case TXFILT_SQUARE:
//bw = 0.9f / (float)k;
bw = 0.4f;
decim_rx = firfilt_crcf_create_kaiser(2*k*m+1, bw, 60.0f, 0.0f);
firfilt_crcf_set_scale(decim_rx, 2.0f * bw);
break;
case TXFILT_RCOS_FULL:
if (M==2) {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k,m,0.5f,0);
firfilt_crcf_set_scale(decim_rx, 1.33f / (float)k);
} else {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k/2,2*m,0.9f,0);
firfilt_crcf_set_scale(decim_rx, 3.25f / (float)k);
}
break;
case TXFILT_RCOS_HALF:
if (M==2) {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k,m,0.3f,0);
firfilt_crcf_set_scale(decim_rx, 1.10f / (float)k);
} else {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k/2,2*m,0.27f,0);
firfilt_crcf_set_scale(decim_rx, 2.90f / (float)k);
}
break;
case TXFILT_GMSK:
bw = 0.5f / (float)k;
// TODO: figure out beta value here
beta = (M == 2) ? 0.8*gmsk_bt : 1.0*gmsk_bt;
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k,m,beta,0);
firfilt_crcf_set_scale(decim_rx, 2.0f * bw);
break;
default:
fprintf(stderr,"error: %s, invalid tx filter type\n", argv[0]);
exit(1);
}
printf("bw = %f\n", bw);
// run receiver
unsigned int n=0;
unsigned int num_errors = 0;
unsigned int num_symbols_checked = 0;
float complex z_prime = 0.0f;
for (i=0; i<num_samples; i++) {
// push through filter
firfilt_crcf_push(decim_rx, y[i]);
firfilt_crcf_execute(decim_rx, &z[i]);
// decimate output
if ( (i%k)==0 ) {
// compute instantaneous frequency scaled by modulation index
float phi_hat = cargf(conjf(z_prime) * z[i]) / (h * M_PI);
// estimate transmitted symbol
float v = (phi_hat + (M-1.0))*0.5f;
unsigned int sym_out = ((int) roundf(v)) % M;
// save current point
z_prime = z[i];
// print result to screen
printf("%3u : %12.8f + j%12.8f, <f=%8.4f : %8.4f> (%1u)",
n, crealf(z[i]), cimagf(z[i]), phi_hat, v, sym_out);
if (n >= m+tx_delay) {
num_errors += (sym_out == sym_in[n-m-tx_delay]) ? 0 : 1;
num_symbols_checked++;
printf(" (%1u)\n", sym_in[n-m-tx_delay]);
} else {
printf("\n");
}
n++;
}
}
// print number of errors
printf("errors : %3u / %3u\n", num_errors, num_symbols_checked);
// destroy objects
firinterp_rrrf_destroy(interp_tx);
firfilt_crcf_destroy(decim_rx);
// compute power spectral density of transmitted signal
unsigned int nfft = 1024;
float psd[nfft];
spgramcf periodogram = spgramcf_create_kaiser(nfft, nfft/2, 8.0f);
spgramcf_estimate_psd(periodogram, y, num_samples, psd);
spgramcf_destroy(periodogram);
//
// 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,"k = %u;\n", k);
fprintf(fid,"h = %f;\n", h);
fprintf(fid,"num_symbols = %u;\n", num_symbols);
fprintf(fid,"num_samples = %u;\n", num_samples);
fprintf(fid,"nfft = %u;\n", nfft);
fprintf(fid,"delay = %u; %% receive filter delay\n", tx_delay);
fprintf(fid,"x = zeros(1,num_samples);\n");
fprintf(fid,"y = zeros(1,num_samples);\n");
fprintf(fid,"z = zeros(1,num_samples);\n");
fprintf(fid,"phi = zeros(1,num_samples);\n");
for (i=0; i<num_samples; i++) {
fprintf(fid,"x(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"z(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(z[i]), cimagf(z[i]));
fprintf(fid,"phi(%4u) = %12.8f;\n", i+1, phi[i]);
}
// save PSD
fprintf(fid,"psd = zeros(1,nfft);\n");
for (i=0; i<nfft; i++)
fprintf(fid,"psd(%4u) = %12.8f;\n", i+1, psd[i]);
fprintf(fid,"t=[0:(num_samples-1)]/k;\n");
fprintf(fid,"i = 1:k:num_samples;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(3,4,1:3);\n");
fprintf(fid," plot(t,real(x),'-', t(i),real(x(i)),'bs','MarkerSize',4,...\n");
fprintf(fid," t,imag(x),'-', t(i),imag(x(i)),'gs','MarkerSize',4);\n");
fprintf(fid," axis([0 num_symbols -1.2 1.2]);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('x(t)');\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,4,5:7);\n");
fprintf(fid," plot(t-delay,real(z),'-', t(i)-delay,real(z(i)),'bs','MarkerSize',4,...\n");
fprintf(fid," t-delay,imag(z),'-', t(i)-delay,imag(z(i)),'gs','MarkerSize',4);\n");
fprintf(fid," axis([0 num_symbols -1.2 1.2]);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('\"matched\" filter output');\n");
fprintf(fid," grid on;\n");
// plot I/Q constellations
fprintf(fid,"subplot(3,4,4);\n");
fprintf(fid," plot(real(y),imag(y),'-',real(y(i)),imag(y(i)),'rs','MarkerSize',3);\n");
fprintf(fid," xlabel('I');\n");
fprintf(fid," ylabel('Q');\n");
fprintf(fid," axis([-1 1 -1 1]*1.2);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,4,8);\n");
fprintf(fid," plot(real(z),imag(z),'-',real(z(i)),imag(z(i)),'rs','MarkerSize',3);\n");
fprintf(fid," xlabel('I');\n");
fprintf(fid," ylabel('Q');\n");
fprintf(fid," axis([-1 1 -1 1]*1.2);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
// plot PSD
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"subplot(3,4,9:12);\n");
fprintf(fid," plot(f,psd,'LineWidth',1.5);\n");
fprintf(fid," axis([-0.5 0.5 -40 20]);\n");
fprintf(fid," xlabel('Normalized Frequency [f/F_s]');\n");
fprintf(fid," ylabel('PSD [dB]');\n");
fprintf(fid," grid on;\n");
#if 0
fprintf(fid,"figure;\n");
fprintf(fid," %% compute instantaneous received frequency\n");
fprintf(fid," freq_rx = arg( conj(z(:)) .* circshift(z(:),-1) )';\n");
fprintf(fid," freq_rx(1:(k*delay)) = 0;\n");
fprintf(fid," freq_rx(end) = 0;\n");
fprintf(fid," %% compute instantaneous tx/rx phase\n");
if (tx_filter_type == TXFILT_SQUARE) {
fprintf(fid," theta_tx = filter([0 1],[1 -1],phi)/(h*pi);\n");
fprintf(fid," theta_rx = filter([0 1],[1 -1],freq_rx)/(h*pi);\n");
} else {
fprintf(fid," theta_tx = filter([0.5 0.5],[1 -1],phi)/(h*pi);\n");
fprintf(fid," theta_rx = filter([0.5 0.5],[1 -1],freq_rx)/(h*pi);\n");
}
fprintf(fid," %% plot instantaneous tx/rx phase\n");
fprintf(fid," plot(t, theta_tx,'-b', t(i), theta_tx(i),'sb',...\n");
fprintf(fid," t-delay,theta_rx,'-r', t(i)-delay,theta_rx(i),'sr');\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('instantaneous phase/(h \\pi)');\n");
fprintf(fid," legend('transmitted','syms','received/filtered','syms','location','northwest');\n");
fprintf(fid," grid on;\n");
#else
// plot filter response
fprintf(fid,"ht_len = %u;\n", ht_len);
fprintf(fid,"ht = zeros(1,ht_len);\n");
for (i=0; i<ht_len; i++)
fprintf(fid,"ht(%4u) = %12.8f;\n", i+1, ht[i]);
fprintf(fid,"gt1 = filter([0.5 0.5],[1 -1],ht) / (pi*h);\n");
fprintf(fid,"gt2 = filter([0.0 1.0],[1 -1],ht) / (pi*h);\n");
fprintf(fid,"tfilt = [0:(ht_len-1)]/k - delay + 0.5;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(tfilt,ht, '-x','MarkerSize',4,...\n");
fprintf(fid," tfilt,gt1,'-x','MarkerSize',4,...\n");
fprintf(fid," tfilt,gt2,'-x','MarkerSize',4);\n");
fprintf(fid,"axis([tfilt(1) tfilt(end) -0.1 1.1]);\n");
fprintf(fid,"legend('pulse','trap. int.','rect. int.','location','northwest');\n");
fprintf(fid,"grid on;\n");
#endif
fclose(fid);
printf("results written to '%s'\n", OUTPUT_FILENAME);
// free allocated filter memory
free(ht);
return 0;
}
ModemKit *ModemFMStereo::buildKit(long long sampleRate, int audioSampleRate) {
ModemKitFMStereo *kit = new ModemKitFMStereo;
kit->audioResampleRatio = double(audioSampleRate) / double(sampleRate);
kit->sampleRate = sampleRate;
kit->audioSampleRate = audioSampleRate;
float As = 60.0f; // stop-band attenuation [dB]
kit->audioResampler = msresamp_rrrf_create(kit->audioResampleRatio, As);
kit->stereoResampler = msresamp_rrrf_create(kit->audioResampleRatio, As);
// Stereo filters / shifters
double firStereoCutoff = 16000.0 / double(audioSampleRate);
// filter transition
float ft = 1000.0f / double(audioSampleRate);
// fractional timing offset
float mu = 0.0f;
if (firStereoCutoff < 0) {
firStereoCutoff = 0;
}
if (firStereoCutoff > 0.5) {
firStereoCutoff = 0.5;
}
unsigned int h_len = estimate_req_filter_len(ft, As);
float *h = new float[h_len];
liquid_firdes_kaiser(h_len, firStereoCutoff, As, mu, h);
kit->firStereoLeft = firfilt_rrrf_create(h, h_len);
kit->firStereoRight = firfilt_rrrf_create(h, h_len);
// stereo pilot filter
float bw = float(sampleRate);
if (bw < 100000.0) {
bw = 100000.0;
}
unsigned int order = 5; // filter order
float f0 = ((float) 19000 / bw);
float fc = ((float) 19500 / bw);
float Ap = 1.0f;
kit->iirStereoPilot = iirfilt_crcf_create_prototype(LIQUID_IIRDES_CHEBY2, LIQUID_IIRDES_BANDPASS, LIQUID_IIRDES_SOS, order, fc, f0, Ap, As);
kit->firStereoR2C = firhilbf_create(5, 60.0f);
kit->firStereoC2R = firhilbf_create(5, 60.0f);
kit->stereoPilot = nco_crcf_create(LIQUID_VCO);
nco_crcf_reset(kit->stereoPilot);
nco_crcf_pll_set_bandwidth(kit->stereoPilot, 0.25f);
kit->demph = _demph;
if (_demph) {
float f = (1.0f / (2.0f * M_PI * double(_demph) * 1e-6));
float t = 1.0f / (2.0f * M_PI * f);
t = 1.0f / (2.0f * float(audioSampleRate) * tan(1.0f / (2.0f * float(audioSampleRate) * t)));
float tb = (1.0f + 2.0f * t * float(audioSampleRate));
float b_demph[2] = { 1.0f / tb, 1.0f / tb };
float a_demph[2] = { 1.0f, (1.0f - 2.0f * t * float(audioSampleRate)) / tb };
kit->iirDemphL = iirfilt_rrrf_create(b_demph, 2, a_demph, 2);
kit->iirDemphR = iirfilt_rrrf_create(b_demph, 2, a_demph, 2);
} else {
kit->iirDemphL = nullptr;
kit->iirDemphR = nullptr;
kit->demph = 0;
}
return kit;
}
// create cpfskmod object (frequency modulator)
// _bps : bits per symbol, _bps > 0
// _h : modulation index, _h > 0
// _k : samples/symbol, _k > 1, _k even
// _m : filter delay (symbols), _m > 0
// _beta : filter bandwidth parameter, _beta > 0
// _type : filter type (e.g. LIQUID_CPFSK_SQUARE)
cpfskmod cpfskmod_create(unsigned int _bps,
float _h,
unsigned int _k,
unsigned int _m,
float _beta,
int _type)
{
// validate input
if (_bps == 0) {
fprintf(stderr,"error: cpfskmod_create(), bits/symbol must be greater than 0\n");
exit(1);
} else if (_k < 2 || (_k%2)) {
fprintf(stderr,"error: cpfskmod_create(), samples/symbol must be greater than 2 and even\n");
exit(1);
} else if (_m == 0) {
fprintf(stderr,"error: cpfskmod_create(), filter delay must be greater than 0\n");
exit(1);
} else if (_beta <= 0.0f || _beta > 1.0f) {
fprintf(stderr,"error: cpfskmod_create(), filter roll-off must be in (0,1]\n");
exit(1);
} else if (_h <= 0.0f) {
fprintf(stderr,"error: cpfskmod_create(), modulation index must be greater than 0\n");
exit(1);
}
// create main object memory
cpfskmod q = (cpfskmod) malloc(sizeof(struct cpfskmod_s));
// set basic internal properties
q->bps = _bps; // bits per symbol
q->h = _h; // modulation index
q->k = _k; // samples per symbol
q->m = _m; // filter delay (symbols)
q->beta = _beta; // filter roll-off factor (only for certain filters)
q->type = _type; // filter type
// derived values
q->M = 1 << q->bps; // constellation size
// create object depending upon input type
float b[2] = {0.5f, 0.5f}; // integrator feed-forward coefficients
float a[2] = {1.0f, -1.0f}; // integrator feed-back coefficients
q->ht_len = 0;
q->ht = NULL;
unsigned int i;
switch(q->type) {
case LIQUID_CPFSK_SQUARE:
q->ht_len = q->k;
q->symbol_delay = 1;
// modify integrator
b[0] = 0.0f;
b[1] = 1.0f;
break;
case LIQUID_CPFSK_RCOS_FULL:
q->ht_len = q->k;
q->symbol_delay = 1;
break;
case LIQUID_CPFSK_RCOS_PARTIAL:
// TODO: adjust reponse based on 'm'
q->ht_len = 3*q->k;
q->symbol_delay = 2;
break;
case LIQUID_CPFSK_GMSK:
q->symbol_delay = q->m + 1;
q->ht_len = 2*(q->k)*(q->m) + (q->k) + 1;
break;
default:
fprintf(stderr,"error: cpfskmodem_create(), invalid filter type '%d'\n", q->type);
exit(1);
}
// create pulse-shaping filter and scale by modulation index
q->ht = (float*) malloc(q->ht_len *sizeof(float));
cpfskmod_firdes(q->k, q->m, q->beta, q->type, q->ht, q->ht_len);
for (i=0; i<q->ht_len; i++)
q->ht[i] *= M_PI * q->h;
q->interp = firinterp_rrrf_create(q->k, q->ht, q->ht_len);
// create phase integrator
q->phase_interp = (float*) malloc(q->k*sizeof(float));
q->integrator = iirfilt_rrrf_create(b,2,a,2);
// reset modem object
cpfskmod_reset(q);
return q;
}
int main() {
// parameters
float phase_offset = 0.8f;
float frequency_offset = 0.01f;
float pll_bandwidth = 0.05f;
float pll_damping_factor = 0.707f;
unsigned int n=256; // number of iterations
unsigned int d=n/32; // print every "d" lines
//
float theta[n]; // input phase
float complex x[n]; // input sinusoid
float phi[n]; // output phase
float complex y[n]; // output sinusoid
// generate iir loop filter(s)
float a[3];
float b[3];
float wn = pll_bandwidth;
float zeta = pll_damping_factor;
float K = 10; // loop gain
#if 0
// loop filter (active lag)
float t1 = K/(wn*wn);
float t2 = 2*zeta/wn - 1/K;
b[0] = 2*K*(1.+t2/2.0f);
b[1] = 2*K*2.;
b[2] = 2*K*(1.-t2/2.0f);
a[0] = 1 + t1/2.0f;
a[1] = -t1;
a[2] = -1 + t1/2.0f;
#else
// loop filter (active PI)
float t1 = K/(wn*wn);
float t2 = 2*zeta/wn;
b[0] = 2*K*(1.+t2/2.0f);
b[1] = 2*K*2.;
b[2] = 2*K*(1.-t2/2.0f);
a[0] = t1/2.0f;
a[1] = -t1;
a[2] = t1/2.0f;
#endif
iirfilt_rrrf H = iirfilt_rrrf_create(b,3,a,3);
iirfilt_rrrf_print(H);
unsigned int i;
// generate input
float t=phase_offset;
float dt = frequency_offset;
for (i=0; i<n; i++) {
theta[i] = t;
x[i] = cexpf(_Complex_I*theta[i]);
t += dt;
}
// run loop
float phi_hat=0.0f;
for (i=0; i<n; i++) {
y[i] = cexpf(_Complex_I*phi_hat);
// compute error
float e = cargf(x[i]*conjf(y[i]));
if ( (i%d)==0 )
printf("e(%3u) = %12.8f;\n", i, e);
// filter error
iirfilt_rrrf_execute(H,e,&phi_hat);
phi[i] = phi_hat;
}
// destroy filter
iirfilt_rrrf_destroy(H);
// open output file
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"clear all;\n");
fprintf(fid,"n=%u;\n",n);
fprintf(fid,"a(1) = %16.8e;\n", a[0]);
fprintf(fid,"a(2) = %16.8e;\n", a[1]);
fprintf(fid,"a(3) = %16.8e;\n", a[2]);
fprintf(fid,"b(1) = %16.8e;\n", b[0]);
fprintf(fid,"b(2) = %16.8e;\n", b[1]);
fprintf(fid,"b(3) = %16.8e;\n", b[2]);
//fprintf(fid,"figure;\n");
//fprintf(fid,"freqz(b,a);\n");
for (i=0; i<n; i++) {
fprintf(fid,"theta(%3u) = %16.8e;\n", i+1, theta[i]);
fprintf(fid," phi(%3u) = %16.8e;\n", i+1, phi[i]);
}
fprintf(fid,"t=0:(n-1);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(t,theta,t,phi);\n");
fprintf(fid,"xlabel('sample index');\n");
fprintf(fid,"ylabel('phase');\n");
fclose(fid);
printf("output written to %s.\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
int main() {
// options
unsigned int n = 200; // input sequence length
unsigned int p = 4; // prediction filter order
// original filter
#if 1
// autoregressive moving average filter
// ./examples/iirdes_example -t butter -n3 -otf -f0.2
float b[4] = {0.01809893, 0.05429679, 0.05429679, 0.01809893};
float a[4] = {1.00000000, -1.76004195, 1.18289328, -0.27805993};
#else
// autoregressive filter
float b[4] = {1.0f, 0.0f, 0.0f, 0.0f};
float a[4] = {1.0f, 0.5f, 0.4f, 0.3f};
#endif
// create filter object
iirfilt_rrrf f = iirfilt_rrrf_create(b,4, a,4);
iirfilt_rrrf_print(f);
unsigned int i;
// allocate memory for data arrays
float x[n]; // input noise sequence
float y[n]; // output filtered noise sequence
float a_hat[p+1]; // lpc output
float g_hat[p+1]; // lpc output
// generate input noise signal
for (i=0; i<n; i++) {
x[i] = randnf();
//x[i] = ( (i%20) == 0 ) ? 1.0f : 0.0f;
}
// run filter
for (i=0; i<n; i++)
iirfilt_rrrf_execute(f, x[i], &y[i]);
// destroy filter object
iirfilt_rrrf_destroy(f);
// run linear prediction algorithm
liquid_lpc(y,n,p,a_hat,g_hat);
// run prediction filter
float a_lpc[p+1];
float b_lpc[p+1];
for (i=0; i<p+1; i++) {
a_lpc[i] = (i==0) ? 1.0f : 0.0f;
b_lpc[i] = (i==0) ? 0.0f : -a_hat[i];
}
f = iirfilt_rrrf_create(b_lpc,p+1, a_lpc,p+1);
iirfilt_rrrf_print(f);
float y_hat[n];
for (i=0; i<n; i++)
iirfilt_rrrf_execute(f, y[i], &y_hat[i]);
iirfilt_rrrf_destroy(f);
// compute prediction error
float err[n];
for (i=0; i<n; i++)
err[i] = y[i] - y_hat[i];
// compute autocorrelation of prediction error
float lag[n];
float rxx[n];
for (i=0; i<n; i++) {
lag[i] = (float)i;
rxx[i] = 0.0f;
unsigned int j;
for (j=i; j<n; j++)
rxx[i] += err[j] * err[j-i];
}
float rxx0 = rxx[0];
for (i=0; i<n; i++)
rxx[i] /= rxx0;
// print results
for (i=0; i<p+1; i++)
printf(" a[%3u] = %12.8f, g[%3u] = %12.8f\n", i, a_hat[i], i, g_hat[i]);
printf(" prediction rmse = %12.8f\n", sqrtf(rxx0 / n));
//
// plot results to 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");
fprintf(fid,"p=%u;\n", p);
fprintf(fid,"n=%u;\n",n);
#if 0
fprintf(fid,"b = zeros(1,p+1);\n");
fprintf(fid,"a = zeros(1,p+1);\n");
for (i=0; i<p+1; i++) {
fprintf(fid,"b(%4u) = %12.4e;\n", i+1, b_lpc[i]);
fprintf(fid,"a(%4u) = %12.4e;\n", i+1, a_lpc[i]);
}
#endif
fprintf(fid,"x = zeros(1,n);\n");
fprintf(fid,"y = zeros(1,n);\n");
fprintf(fid,"y_hat = zeros(1,n);\n");
fprintf(fid,"lag = zeros(1,n);\n");
fprintf(fid,"rxx = zeros(1,n);\n");
for (i=0; i<n; i++) {
fprintf(fid,"x(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"y_hat(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(y_hat[i]), cimagf(y_hat[i]));
fprintf(fid,"lag(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(lag[i]), cimagf(lag[i]));
fprintf(fid,"rxx(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(rxx[i]), cimagf(rxx[i]));
}
// plot output
fprintf(fid,"t=0:(n-1);\n");
fprintf(fid,"figure;\n");
fprintf(fid," plot(t,x,'-','Color',[1 1 1]*0.5,'LineWidth',1,...\n");
fprintf(fid," t,y,'-','Color',[0 0.5 0.25],'LineWidth',2);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('real');\n");
fprintf(fid," legend('input','filtered output',1);\n");
fprintf(fid," grid on;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(5,1,1:3);\n");
fprintf(fid," plot(t,y,t,y_hat);\n");
fprintf(fid," ylabel('signal');\n");
fprintf(fid," legend('y','lpc estimate',1);\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(5,1,4);\n");
fprintf(fid," plot(t,y-y_hat);\n");
fprintf(fid," ylabel('error');\n");
fprintf(fid,"subplot(5,1,5);\n");
fprintf(fid," plot(t,rxx);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('r_{xx}(e)');\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
