/* -*- c++ -*- */ /* * Copyright 2002,2007,2008,2012 Free Software Foundation, Inc. * * This file is part of GNU Radio * * GNU Radio is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3, or (at your option) * any later version. * * GNU Radio is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with GNU Radio; see the file COPYING. If not, write to * the Free Software Foundation, Inc., 51 Franklin Street, * Boston, MA 02110-1301, USA. */ #ifdef HAVE_CONFIG_H #include #endif #include #include using std::vector; namespace gr { namespace filter { #define IzeroEPSILON 1E-21 /* Max error acceptable in Izero */ static double Izero(double x) { double sum, u, halfx, temp; int n; sum = u = n = 1; halfx = x/2.0; do { temp = halfx/(double)n; n += 1; temp *= temp; u *= temp; sum += u; } while (u >= IzeroEPSILON*sum); return(sum); } // // === Low Pass === // vector firdes::low_pass_2(double gain, double sampling_freq, // Hz double cutoff_freq, // Hz BEGINNING of transition band double transition_width, // Hz width of transition band double attenuation_dB, // attenuation dB win_type window_type, double beta) // used only with Kaiser { sanity_check_1f(sampling_freq, cutoff_freq, transition_width); int ntaps = compute_ntaps_windes(sampling_freq, transition_width, attenuation_dB); // construct the truncated ideal impulse response // [sin(x)/x for the low pass case] vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if (n == 0) taps[n + M] = fwT0 / M_PI * w[n + M]; else { // a little algebra gets this into the more familiar sin(x)/x form taps[n + M] = sin(n * fwT0) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For low-pass, gain @ zero freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M]; gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } vector firdes::low_pass(double gain, double sampling_freq, double cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band win_type window_type, double beta) // used only with Kaiser { sanity_check_1f(sampling_freq, cutoff_freq, transition_width); int ntaps = compute_ntaps(sampling_freq, transition_width, window_type, beta); // construct the truncated ideal impulse response // [sin(x)/x for the low pass case] vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if(n == 0) taps[n + M] = fwT0 / M_PI * w[n + M]; else { // a little algebra gets this into the more familiar sin(x)/x form taps[n + M] = sin(n * fwT0) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For low-pass, gain @ zero freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M]; gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } // // === High Pass === // vector firdes::high_pass_2(double gain, double sampling_freq, double cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band double attenuation_dB, // attenuation dB win_type window_type, double beta) // used only with Kaiser { sanity_check_1f(sampling_freq, cutoff_freq, transition_width); int ntaps = compute_ntaps_windes(sampling_freq, transition_width, attenuation_dB); // construct the truncated ideal impulse response times the window function vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if(n == 0) taps[n + M] = (1 - (fwT0 / M_PI)) * w[n + M]; else { // a little algebra gets this into the more familiar sin(x)/x form taps[n + M] = -sin(n * fwT0) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For high-pass, gain @ fs/2 freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M] * cos(n * M_PI); gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } vector firdes::high_pass(double gain, double sampling_freq, double cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band win_type window_type, double beta) // used only with Kaiser { sanity_check_1f(sampling_freq, cutoff_freq, transition_width); int ntaps = compute_ntaps(sampling_freq, transition_width, window_type, beta); // construct the truncated ideal impulse response times the window function vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if(n == 0) taps[n + M] = (1 - (fwT0 / M_PI)) * w[n + M]; else { // a little algebra gets this into the more familiar sin(x)/x form taps[n + M] = -sin(n * fwT0) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For high-pass, gain @ fs/2 freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M] * cos(n * M_PI); gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } // // === Band Pass === // vector firdes::band_pass_2(double gain, double sampling_freq, double low_cutoff_freq, // Hz center of transition band double high_cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band double attenuation_dB, // attenuation dB win_type window_type, double beta) // used only with Kaiser { sanity_check_2f(sampling_freq, low_cutoff_freq, high_cutoff_freq, transition_width); int ntaps = compute_ntaps_windes(sampling_freq, transition_width, attenuation_dB); vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * low_cutoff_freq / sampling_freq; double fwT1 = 2 * M_PI * high_cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if (n == 0) taps[n + M] = (fwT1 - fwT0) / M_PI * w[n + M]; else { taps[n + M] = (sin(n * fwT1) - sin(n * fwT0)) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For band-pass, gain @ center freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M] * cos(n * (fwT0 + fwT1) * 0.5); gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } vector firdes::band_pass(double gain, double sampling_freq, double low_cutoff_freq, // Hz center of transition band double high_cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band win_type window_type, double beta) // used only with Kaiser { sanity_check_2f(sampling_freq, low_cutoff_freq, high_cutoff_freq, transition_width); int ntaps = compute_ntaps(sampling_freq, transition_width, window_type, beta); // construct the truncated ideal impulse response times the window function vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * low_cutoff_freq / sampling_freq; double fwT1 = 2 * M_PI * high_cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if (n == 0) taps[n + M] = (fwT1 - fwT0) / M_PI * w[n + M]; else { taps[n + M] = (sin(n * fwT1) - sin(n * fwT0)) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For band-pass, gain @ center freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M] * cos(n * (fwT0 + fwT1) * 0.5); gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } // // === Complex Band Pass === // vector firdes::complex_band_pass_2(double gain, double sampling_freq, double low_cutoff_freq, // Hz center of transition band double high_cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band double attenuation_dB, // attenuation dB win_type window_type, double beta) // used only with Kaiser { sanity_check_2f_c(sampling_freq, low_cutoff_freq, high_cutoff_freq, transition_width); int ntaps = compute_ntaps_windes(sampling_freq, transition_width, attenuation_dB); vector taps(ntaps); vector lptaps(ntaps); vector w = window(window_type, ntaps, beta); lptaps = low_pass_2(gain, sampling_freq, (high_cutoff_freq - low_cutoff_freq)/2, transition_width, attenuation_dB, window_type, beta); gr_complex *optr = &taps[0]; float *iptr = &lptaps[0]; float freq = M_PI * (high_cutoff_freq + low_cutoff_freq)/sampling_freq; float phase = 0; if (lptaps.size() & 01) { phase = - freq * ( lptaps.size() >> 1 ); } else phase = - freq/2.0 * ((1 + 2*lptaps.size()) >> 1); for(unsigned int i = 0; i < lptaps.size(); i++) { *optr++ = gr_complex(*iptr * cos(phase), *iptr * sin(phase)); iptr++, phase += freq; } return taps; } vector firdes::complex_band_pass(double gain, double sampling_freq, double low_cutoff_freq, // Hz center of transition band double high_cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band win_type window_type, double beta) // used only with Kaiser { sanity_check_2f_c (sampling_freq, low_cutoff_freq, high_cutoff_freq, transition_width); int ntaps = compute_ntaps(sampling_freq, transition_width, window_type, beta); // construct the truncated ideal impulse response times the window function vector taps(ntaps); vector lptaps(ntaps); vector w = window(window_type, ntaps, beta); lptaps = low_pass(gain, sampling_freq, (high_cutoff_freq - low_cutoff_freq)/2, transition_width, window_type, beta); gr_complex *optr = &taps[0]; float *iptr = &lptaps[0]; float freq = M_PI * (high_cutoff_freq + low_cutoff_freq)/sampling_freq; float phase = 0; if(lptaps.size() & 01) { phase = - freq * ( lptaps.size() >> 1 ); } else phase = - freq/2.0 * ((1 + 2*lptaps.size()) >> 1); for(unsigned int i=0;i firdes::band_reject_2(double gain, double sampling_freq, double low_cutoff_freq, // Hz center of transition band double high_cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band double attenuation_dB, // attenuation dB win_type window_type, double beta) // used only with Kaiser { sanity_check_2f(sampling_freq, low_cutoff_freq, high_cutoff_freq, transition_width); int ntaps = compute_ntaps_windes(sampling_freq, transition_width, attenuation_dB); // construct the truncated ideal impulse response times the window function vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * low_cutoff_freq / sampling_freq; double fwT1 = 2 * M_PI * high_cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if (n == 0) taps[n + M] = 1.0 + ((fwT0 - fwT1) / M_PI * w[n + M]); else { taps[n + M] = (sin(n * fwT0) - sin(n * fwT1)) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For band-reject, gain @ zero freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M]; gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } vector firdes::band_reject(double gain, double sampling_freq, double low_cutoff_freq, // Hz center of transition band double high_cutoff_freq, // Hz center of transition band double transition_width, // Hz width of transition band win_type window_type, double beta) // used only with Kaiser { sanity_check_2f(sampling_freq, low_cutoff_freq, high_cutoff_freq, transition_width); int ntaps = compute_ntaps(sampling_freq, transition_width, window_type, beta); // construct the truncated ideal impulse response times the window function vector taps(ntaps); vector w = window(window_type, ntaps, beta); int M = (ntaps - 1) / 2; double fwT0 = 2 * M_PI * low_cutoff_freq / sampling_freq; double fwT1 = 2 * M_PI * high_cutoff_freq / sampling_freq; for(int n = -M; n <= M; n++) { if (n == 0) taps[n + M] = 1.0 + ((fwT0 - fwT1) / M_PI * w[n + M]); else { taps[n + M] = (sin(n * fwT0) - sin(n * fwT1)) / (n * M_PI) * w[n + M]; } } // find the factor to normalize the gain, fmax. // For band-reject, gain @ zero freq = 1.0 double fmax = taps[0 + M]; for(int n = 1; n <= M; n++) fmax += 2 * taps[n + M]; gain /= fmax; // normalize for(int i = 0; i < ntaps; i++) taps[i] *= gain; return taps; } // // Hilbert Transform // vector firdes::hilbert(unsigned int ntaps, win_type windowtype, double beta) { if(!(ntaps & 1)) throw std::out_of_range("Hilbert: Must have odd number of taps"); vector taps(ntaps); vector w = window (windowtype, ntaps, beta); unsigned int h = (ntaps-1)/2; float gain=0; for(unsigned int i = 1; i <= h; i++) { if(i & 1) { float x = 1/(float)i; taps[h+i] = x * w[h+i]; taps[h-i] = -x * w[h-i]; gain = taps[h+i] - gain; } else taps[h+i] = taps[h-i] = 0; } gain = 2 * fabs(gain); for(unsigned int i = 0; i < ntaps; i++) taps[i] /= gain; return taps; } // // Gaussian // vector firdes::gaussian(double gain, double spb, double bt, int ntaps) { vector taps(ntaps); double scale = 0; double dt = 1.0/spb; double s = 1.0/(sqrt(log(2.0)) / (2*M_PI*bt)); double t0 = -0.5 * ntaps; double ts; for(int i=0;i firdes::root_raised_cosine(double gain, double sampling_freq, double symbol_rate, double alpha, int ntaps) { ntaps |= 1; // ensure that ntaps is odd double spb = sampling_freq/symbol_rate; // samples per bit/symbol vector taps(ntaps); double scale = 0; for(int i = 0; i < ntaps; i++) { double x1,x2,x3,num,den; double xindx = i - ntaps/2; x1 = M_PI * xindx/spb; x2 = 4 * alpha * xindx / spb; x3 = x2*x2 - 1; if(fabs(x3) >= 0.000001) { // Avoid Rounding errors... if(i != ntaps/2) num = cos((1+alpha)*x1) + sin((1-alpha)*x1)/(4*alpha*xindx/spb); else num = cos((1+alpha)*x1) + (1-alpha) * M_PI / (4*alpha); den = x3 * M_PI; } else { if(alpha==1) { taps[i] = -1; continue; } x3 = (1-alpha)*x1; x2 = (1+alpha)*x1; num = (sin(x2)*(1+alpha)*M_PI - cos(x3)*((1-alpha)*M_PI*spb)/(4*alpha*xindx) + sin(x3)*spb*spb/(4*alpha*xindx*xindx)); den = -32 * M_PI * alpha * alpha * xindx/spb; } taps[i] = 4 * alpha * num / den; scale += taps[i]; } for(int i = 0; i < ntaps; i++) taps[i] = taps[i] * gain / scale; return taps; } // // === Utilities === // // delta_f / width_factor gives number of taps required. static const float width_factor[5] = { // indexed by win_type 3.3, // WIN_HAMMING 3.1, // WIN_HANN 5.5, // WIN_BLACKMAN 2.0, // WIN_RECTANGULAR //5.0 // WIN_KAISER (guesstimate compromise) //2.0 // WIN_KAISER (guesstimate compromise) 10.0 // WIN_KAISER }; int firdes::compute_ntaps_windes(double sampling_freq, double transition_width, // this is frequency, not relative frequency double attenuation_dB) { // Based on formula from Multirate Signal Processing for // Communications Systems, fredric j harris int ntaps = (int)(attenuation_dB*sampling_freq/(22.0*transition_width)); if ((ntaps & 1) == 0) // if even... ntaps++; // ...make odd return ntaps; } int firdes::compute_ntaps(double sampling_freq, double transition_width, win_type window_type, double beta) { // normalized transition width double delta_f = transition_width / sampling_freq; // compute number of taps required for given transition width int ntaps = (int)(width_factor[window_type] / delta_f + 0.5); if((ntaps & 1) == 0) // if even... ntaps++; // ...make odd return ntaps; } double firdes::bessi0(double x) { double ax,ans; double y; ax=fabs(x); if (ax < 3.75) { y=x/3.75; y*=y; ans=1.0+y*(3.5156229+y*(3.0899424+y*(1.2067492 +y*(0.2659732+y*(0.360768e-1+y*0.45813e-2))))); } else { y=3.75/ax; ans=(exp(ax)/sqrt(ax))*(0.39894228+y*(0.1328592e-1 +y*(0.225319e-2+y*(-0.157565e-2+y*(0.916281e-2 +y*(-0.2057706e-1+y*(0.2635537e-1+y*(-0.1647633e-1 +y*0.392377e-2)))))))); } return ans; } vector firdes::window (win_type type, int ntaps, double beta) { vector taps(ntaps); int M = ntaps - 1; // filter order switch (type) { case WIN_RECTANGULAR: for(int n = 0; n < ntaps; n++) taps[n] = 1; case WIN_HAMMING: for(int n = 0; n < ntaps; n++) taps[n] = 0.54 - 0.46 * cos((2 * M_PI * n) / M); break; case WIN_HANN: for(int n = 0; n < ntaps; n++) taps[n] = 0.5 - 0.5 * cos((2 * M_PI * n) / M); break; case WIN_BLACKMAN: for(int n = 0; n < ntaps; n++) taps[n] = 0.42 - 0.50 * cos((2*M_PI * n) / (M-1)) - 0.08 * cos((4*M_PI * n) / (M-1)); break; case WIN_BLACKMAN_hARRIS: for(int n = -ntaps/2; n < ntaps/2; n++) taps[n+ntaps/2] = 0.35875 + 0.48829*cos((2*M_PI * n) / (float)M) + 0.14128*cos((4*M_PI * n) / (float)M) + 0.01168*cos((6*M_PI * n) / (float)M); break; case WIN_KAISER: { double IBeta = 1.0/Izero(beta); double inm1 = 1.0/((double)(ntaps)); double temp; //fprintf(stderr, "IBeta = %g; inm1 = %g\n", IBeta, inm1); for(int i=0; i 0"); if(fa <= 0.0 || fa > sampling_freq / 2) throw std::out_of_range("firdes check failed: 0 < fa <= sampling_freq / 2"); if(transition_width <= 0) throw std::out_of_range("gr_dirdes check failed: transition_width > 0"); } void firdes::sanity_check_2f(double sampling_freq, double fa, // first cutoff freq double fb, // second cutoff freq double transition_width) { if (sampling_freq <= 0.0) throw std::out_of_range("firdes check failed: sampling_freq > 0"); if (fa <= 0.0 || fa > sampling_freq / 2) throw std::out_of_range("firdes check failed: 0 < fa <= sampling_freq / 2"); if (fb <= 0.0 || fb > sampling_freq / 2) throw std::out_of_range("firdes check failed: 0 < fb <= sampling_freq / 2"); if (fa > fb) throw std::out_of_range("firdes check failed: fa <= fb"); if (transition_width <= 0) throw std::out_of_range("firdes check failed: transition_width > 0"); } void firdes::sanity_check_2f_c(double sampling_freq, double fa, // first cutoff freq double fb, // second cutoff freq double transition_width) { if(sampling_freq <= 0.0) throw std::out_of_range("firdes check failed: sampling_freq > 0"); if(fa < -sampling_freq / 2 || fa > sampling_freq / 2) throw std::out_of_range("firdes check failed: 0 < fa <= sampling_freq / 2"); if(fb < -sampling_freq / 2 || fb > sampling_freq / 2) throw std::out_of_range("firdes check failed: 0 < fb <= sampling_freq / 2"); if(fa > fb) throw std::out_of_range("firdes check failed: fa <= fb"); if(transition_width <= 0) throw std::out_of_range("firdes check failed: transition_width > 0"); } } /* namespace filter */ } /* namespace gr */