// create a resamp2 object
// _m : filter semi-length (effective length: 4*_m+1)
// _fc : center frequency of half-band filter
// _As : stop-band attenuation [dB], _As > 0
RESAMP2() RESAMP2(_create)(unsigned int _m,
float _fc,
float _As)
{
// validate input
if (_m < 2) {
fprintf(stderr,"error: resamp2_%s_create(), filter semi-length must be at least 2\n", EXTENSION_FULL);
exit(1);
}
RESAMP2() q = (RESAMP2()) malloc(sizeof(struct RESAMP2(_s)));
q->m = _m;
q->fc = _fc;
q->As = _As;
if ( q->fc < -0.5f || q->fc > 0.5f ) {
fprintf(stderr,"error: resamp2_%s_create(), fc (%12.4e) must be in (-1,1)\n", EXTENSION_FULL, q->fc);
exit(1);
}
// change filter length as necessary
q->h_len = 4*(q->m) + 1;
q->h = (TC *) malloc((q->h_len)*sizeof(TC));
q->h1_len = 2*(q->m);
q->h1 = (TC *) malloc((q->h1_len)*sizeof(TC));
// design filter prototype
unsigned int i;
float t, h1, h2;
TC h3;
float beta = kaiser_beta_As(q->As);
for (i=0; i<q->h_len; i++) {
t = (float)i - (float)(q->h_len-1)/2.0f;
h1 = sincf(t/2.0f);
h2 = kaiser(i,q->h_len,beta,0);
#if TC_COMPLEX == 1
h3 = cosf(2.0f*M_PI*t*q->fc) + _Complex_I*sinf(2.0f*M_PI*t*q->fc);
#else
h3 = cosf(2.0f*M_PI*t*q->fc);
#endif
q->h[i] = h1*h2*h3;
}
// resample, alternate sign, [reverse direction]
unsigned int j=0;
for (i=1; i<q->h_len; i+=2)
q->h1[j++] = q->h[q->h_len - i - 1];
// create dotprod object
q->dp = DOTPROD(_create)(q->h1, 2*q->m);
// create window buffers
q->w0 = WINDOW(_create)(2*(q->m));
q->w1 = WINDOW(_create)(2*(q->m));
RESAMP2(_clear)(q);
return q;
}
// parameterized function
float gsfunc(float _x, float * _v)
{
float c0 = _v[0];
float c1 = _v[1];
float c2 = _v[2];
return c0 + sincf(c1*(_x-c2));
}
// Design FIR using kaiser window
// _n : filter length, _n > 0
// _fc : cutoff frequency, 0 < _fc < 0.5
// _As : stop-band attenuation [dB], _As > 0
// _mu : fractional sample offset, -0.5 < _mu < 0.5
// _h : output coefficient buffer, [size: _n x 1]
void liquid_firdes_kaiser(unsigned int _n,
float _fc,
float _As,
float _mu,
float *_h)
{
// validate inputs
if (_mu < -0.5f || _mu > 0.5f) {
fprintf(stderr,"error: liquid_firdes_kaiser(), _mu (%12.4e) out of range [-0.5,0.5]\n", _mu);
exit(1);
} else if (_fc < 0.0f || _fc > 0.5f) {
fprintf(stderr,"error: liquid_firdes_kaiser(), cutoff frequency (%12.4e) out of range (0, 0.5)\n", _fc);
exit(1);
} else if (_n == 0) {
fprintf(stderr,"error: liquid_firdes_kaiser(), filter length must be greater than zero\n");
exit(1);
}
// choose kaiser beta parameter (approximate)
float beta = kaiser_beta_As(_As);
float t, h1, h2;
unsigned int i;
for (i=0; i<_n; i++) {
t = (float)i - (float)(_n-1)/2 + _mu;
// sinc prototype
h1 = sincf(2.0f*_fc*t);
// kaiser window
h2 = kaiser(i,_n,beta,_mu);
//printf("t = %f, h1 = %f, h2 = %f\n", t, h1, h2);
// composite
_h[i] = h1*h2;
}
}
int main() {
// options
unsigned int num_samples = 400; // number of samples
float sig = 0.1f; // noise variance
unsigned int num_iterations = 1000; // number of iterations to run
float v[3] = {1, 1, 1};
unsigned int i;
// range
float xmin = 0.0f;
float xmax = 6.0f;
float dx = (xmax - xmin) / (num_samples-1);
// generate data set
float x[num_samples];
float y[num_samples];
for (i=0; i<num_samples; i++) {
x[i] = xmin + i*dx;
y[i] = sincf(x[i]) + randnf()*sig;
}
struct gsdataset q = {x, y, num_samples};
// create gradsearch object
gradsearchprops_s gsprops;
gradsearchprops_init_default(&gsprops);
gsprops.delta = 1e-6f; // gradient approximation step size
gsprops.gamma = 0.002f; // vector step size
gsprops.alpha = 0.1f; // momentum parameter
gsprops.mu = 0.999f; // decremental gamma paramter (best if not exactly 1.0)
gradsearch gs = gradsearch_create((void*)&q, v, 3, gserror, LIQUID_OPTIM_MINIMIZE, &gsprops);
float rmse;
// execute search
//rmse = gradsearch_run(gs, num_iterations, -1e-6f);
// 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");
// execute search one iteration at a time
fprintf(fid,"u = zeros(1,%u);\n", num_iterations);
for (i=0; i<num_iterations; i++) {
rmse = gserror((void*)&q,v,3);
fprintf(fid,"u(%3u) = %12.4e;\n", i+1, rmse);
gradsearch_step(gs);
if (((i+1)%100)==0)
gradsearch_print(gs);
}
// print results
printf("\n");
gradsearch_print(gs);
printf(" c0 = %12.8f, opt = 1\n", v[0]);
printf(" c1 = %12.8f, opt = 0\n", v[1]);
printf(" c2 = %12.8f, opt = 1\n", v[2]);
printf(" rmse = %12.4e\n", rmse);
fprintf(fid,"figure;\n");
fprintf(fid,"semilogy(u);\n");
fprintf(fid,"xlabel('iteration');\n");
fprintf(fid,"ylabel('error');\n");
fprintf(fid,"title('gradient search results');\n");
fprintf(fid,"grid on;\n");
// save sampled data set
for (i=0; i<num_samples; i++) {
fprintf(fid," x(%4u) = %12.8f;\n", i+1, x[i]);
fprintf(fid," y(%4u) = %12.8f;\n", i+1, y[i]);
fprintf(fid," y_hat(%4u) = %12.8f;\n", i+1, gsfunc(x[i],v));
}
fprintf(fid,"figure;\n");
fprintf(fid,"plot(x,y,'x', x,y_hat,'-');\n");
fprintf(fid,"xlabel('x');\n");
fprintf(fid,"ylabel('f(x)');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('data','fit',1);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
gradsearch_destroy(gs);
return 0;
}
//
// AUTOTEST: sincf
//
void autotest_sincf()
{
float tol = 1e-3f;
CONTEND_DELTA(sincf(0.0f), 1.0f, tol);
}
