// 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;
}
// 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;
}
}
// Design frequency-shifted root-Nyquist filter based on
// the Kaiser-windowed sinc using approximation for rho.
//
// _k : filter over-sampling rate (samples/symbol)
// _m : filter delay (symbols)
// _beta : filter excess bandwidth factor (0,1)
// _dt : filter fractional sample delay
// _h : resulting filter [size: 2*_k*_m+1]
void liquid_firdes_arkaiser(unsigned int _k,
unsigned int _m,
float _beta,
float _dt,
float * _h)
{
// validate input
if (_k < 2) {
fprintf(stderr,"error: liquid_firdes_arkaiser(), k must be at least 2\n");
exit(1);
} else if (_m < 1) {
fprintf(stderr,"error: liquid_firdes_arkaiser(), m must be at least 1\n");
exit(1);
} else if (_beta <= 0.0f || _beta >= 1.0f) {
fprintf(stderr,"error: liquid_firdes_arkaiser(), beta must be in (0,1)\n");
exit(1);
} else if (_dt < -1.0f || _dt > 1.0f) {
fprintf(stderr,"error: liquid_firdes_arkaiser(), dt must be in [-1,1]\n");
exit(1);
}
#if 0
// compute bandwidth adjustment estimate
float rho_hat = rkaiser_approximate_rho(_m,_beta); // bandwidth correction factor
#else
// rho ~ c0 + c1*log(_beta) + c2*log^2(_beta)
// c0 ~ 0.762886 + 0.067663*log(m)
// c1 ~ 0.065515
// c2 ~ log( 1 - 0.088*m^-1.6 )
float c0 = 0.762886 + 0.067663*logf(_m);
float c1 = 0.065515;
float c2 = logf( 1 - 0.088*powf(_m,-1.6 ) );
float log_beta = logf(_beta);
float rho_hat = c0 + c1*log_beta + c2*log_beta*log_beta;
// ensure range is valid
if (rho_hat <= 0.0f || rho_hat >= 1.0f)
rho_hat = rkaiser_approximate_rho(_m,_beta);
#endif
unsigned int n=2*_k*_m+1; // filter length
float kf = (float)_k; // samples/symbol (float)
float del = _beta*rho_hat / kf; // transition bandwidth
float As = estimate_req_filter_As(del, n); // stop-band suppression
float fc = 0.5f*(1 + _beta*(1.0f-rho_hat))/kf; // filter cutoff
#if DEBUG_RKAISER
printf("rho-hat : %12.8f (compare to %12.8f)\n", rho_hat, rkaiser_approximate_rho(_m,_beta));
printf("fc : %12.8f\n", fc);
printf("delta-f : %12.8f\n", del);
printf("As : %12.8f dB\n", As);
printf("alpha : %12.8f\n", kaiser_beta_As(As));
#endif
// compute filter coefficients
liquid_firdes_kaiser(n,fc,As,_dt,_h);
// normalize coefficients
float e2 = 0.0f;
unsigned int i;
for (i=0; i<n; i++) e2 += _h[i]*_h[i];
for (i=0; i<n; i++) _h[i] *= sqrtf(_k/e2);
}
