// compute filter coefficients and determine resulting ISI
//
// _k : filter over-sampling rate (samples/symbol)
// _m : filter delay (symbols)
// _beta : filter excess bandwidth factor (0,1)
// _dt : filter fractional sample delay
// _rho : transition bandwidth adjustment, 0 < _rho < 1
// _h : filter buffer [size: 2*_k*_m+1]
float liquid_firdes_rkaiser_internal_isi(unsigned int _k,
unsigned int _m,
float _beta,
float _dt,
float _rho,
float * _h)
{
// validate input
if (_rho < 0.0f) {
fprintf(stderr,"warning: liquid_firdes_rkaiser_internal_isi(), rho < 0\n");
} else if (_rho > 1.0f) {
fprintf(stderr,"warning: liquid_firdes_rkaiser_internal_isi(), rho > 1\n");
}
unsigned int n=2*_k*_m+1; // filter length
float kf = (float)_k; // samples/symbol (float)
float del = _beta*_rho / kf; // transition bandwidth
float As = estimate_req_filter_As(del, n); // stop-band suppression
float fc = 0.5f*(1 + _beta*(1.0f-_rho))/kf; // filter cutoff
// evaluate performance (ISI)
float isi_max;
float isi_rms;
// compute filter
liquid_firdes_kaiser(n,fc,As,_dt,_h);
// compute filter ISI
liquid_filter_isi(_h,_k,_m,&isi_rms,&isi_max);
// return RMS of ISI
return isi_rms;
}
// 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);
}
// Design (root-)Nyquist filter from prototype
// _type : filter type (e.g. LIQUID_FIRFILT_RRRC)
// _k : samples/symbol
// _m : symbol delay
// _beta : excess bandwidth factor, _beta in [0,1]
// _dt : fractional sample delay
// _h : output coefficient buffer (length: 2*k*m+1)
void liquid_firdes_prototype(liquid_firfilt_type _type,
unsigned int _k,
unsigned int _m,
float _beta,
float _dt,
float * _h)
{
// compute filter parameters
unsigned int h_len = 2*_k*_m + 1; // length
float fc = 0.5f / (float)_k; // cut-off frequency
float df = _beta / (float)_k; // transition bandwidth
float As = estimate_req_filter_As(df,h_len); // stop-band attenuation
// Parks-McClellan algorithm parameters
float bands[6] = { 0.0f, fc-0.5f*df,
fc, fc,
fc+0.5f*df, 0.5f};
float des[3] = { (float)_k, 0.5f*_k, 0.0f };
float weights[3] = {1.0f, 1.0f, 1.0f};
liquid_firdespm_wtype wtype[3] = { LIQUID_FIRDESPM_FLATWEIGHT,
LIQUID_FIRDESPM_FLATWEIGHT,
LIQUID_FIRDESPM_FLATWEIGHT};
switch (_type) {
// Nyquist filter prototypes
case LIQUID_FIRFILT_KAISER:
liquid_firdes_kaiser(h_len, fc, As, _dt, _h);
break;
case LIQUID_FIRFILT_PM:
// WARNING: input timing offset is ignored here
firdespm_run(h_len, 3, bands, des, weights, wtype, LIQUID_FIRDESPM_BANDPASS, _h);
break;
case LIQUID_FIRFILT_RCOS:
liquid_firdes_rcos(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FEXP:
liquid_firdes_fexp(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FSECH:
liquid_firdes_fsech(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FARCSECH:
liquid_firdes_farcsech(_k, _m, _beta, _dt, _h);
break;
// root-Nyquist filter prototypes
case LIQUID_FIRFILT_ARKAISER:
liquid_firdes_arkaiser(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RKAISER:
liquid_firdes_rkaiser(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RRC:
liquid_firdes_rrcos(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_hM3:
liquid_firdes_hM3(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_GMSKTX:
liquid_firdes_gmsktx(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_GMSKRX:
liquid_firdes_gmskrx(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFEXP:
liquid_firdes_rfexp(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFSECH:
liquid_firdes_rfsech(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFARCSECH:
liquid_firdes_rfarcsech(_k, _m, _beta, _dt, _h);
break;
default:
fprintf(stderr,"error: liquid_firdes_prototype(), invalid root-Nyquist filter type '%d'\n", _type);
exit(1);
}
}
