/* libSoX Biquad filter effects (c) 2006-8 robs@users.sourceforge.net * * This library is free software; you can redistribute it and/or modify it * under the terms of the GNU Lesser General Public License as published by * the Free Software Foundation; either version 2.1 of the License, or (at * your option) any later version. * * This library 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 Lesser * General Public License for more details. * * You should have received a copy of the GNU Lesser General Public License * along with this library; if not, write to the Free Software Foundation, * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA * * * 2-pole filters designed by Robert Bristow-Johnson * see https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html * * 1-pole filters based on code (c) 2000 Chris Bagwell * Algorithms: Recursive single pole low/high pass filter * Reference: The Scientist and Engineer's Guide to Digital Signal Processing * * low-pass: output[N] = input[N] * A + output[N-1] * B * X = exp(-2.0 * pi * Fc) * A = 1 - X * B = X * Fc = cutoff freq / sample rate * * Mimics an RC low-pass filter: * * ---/\/\/\/\-----------> * | * --- C * --- * | * | * V * * high-pass: output[N] = A0 * input[N] + A1 * input[N-1] + B1 * output[N-1] * X = exp(-2.0 * pi * Fc) * A0 = (1 + X) / 2 * A1 = -(1 + X) / 2 * B1 = X * Fc = cutoff freq / sample rate * * Mimics an RC high-pass filter: * * || C * ----||---------> * || | * < * > R * < * | * V */ #include "biquad.h" #include #include typedef biquad_t priv_t; static int hilo1_getopts(sox_effect_t * effp, int argc, char **argv) { return lsx_biquad_getopts(effp, argc, argv, 1, 1, 0, 1, 2, "", *effp->handler.name == 'l'? filter_LPF_1 : filter_HPF_1); } static int hilo2_getopts(sox_effect_t * effp, int argc, char **argv) { priv_t * p = (priv_t *)effp->priv; if (argc > 1 && strcmp(argv[1], "-1") == 0) return hilo1_getopts(effp, argc - 1, argv + 1); if (argc > 1 && strcmp(argv[1], "-2") == 0) ++argv, --argc; p->width = sqrt(0.5); /* Default to Butterworth */ return lsx_biquad_getopts(effp, argc, argv, 1, 2, 0, 1, 2, "qohk", *effp->handler.name == 'l'? filter_LPF : filter_HPF); } static int bandpass_getopts(sox_effect_t * effp, int argc, char **argv) { filter_t type = filter_BPF; if (argc > 1 && strcmp(argv[1], "-c") == 0) ++argv, --argc, type = filter_BPF_CSG; return lsx_biquad_getopts(effp, argc, argv, 2, 2, 0, 1, 2, "hkqob", type); } static int bandrej_getopts(sox_effect_t * effp, int argc, char **argv) { return lsx_biquad_getopts(effp, argc, argv, 2, 2, 0, 1, 2, "hkqob", filter_notch); } static int allpass_getopts(sox_effect_t * effp, int argc, char **argv) { filter_t type = filter_APF; int m; if (argc > 1 && strcmp(argv[1], "-1") == 0) ++argv, --argc, type = filter_AP1; else if (argc > 1 && strcmp(argv[1], "-2") == 0) ++argv, --argc, type = filter_AP2; m = 1 + (type == filter_APF); return lsx_biquad_getopts(effp, argc, argv, m, m, 0, 1, 2, "hkqo", type); } static int tone_getopts(sox_effect_t * effp, int argc, char **argv) { priv_t * p = (priv_t *)effp->priv; p->width = 0.5; p->fc = *effp->handler.name == 'b'? 100 : 3000; return lsx_biquad_getopts(effp, argc, argv, 1, 3, 1, 2, 0, "shkqo", *effp->handler.name == 'b'? filter_lowShelf: filter_highShelf); } static int equalizer_getopts(sox_effect_t * effp, int argc, char **argv) { return lsx_biquad_getopts(effp, argc, argv, 3, 3, 0, 1, 2, "qohk", filter_peakingEQ); } static int band_getopts(sox_effect_t * effp, int argc, char **argv) { filter_t type = filter_BPF_SPK; if (argc > 1 && strcmp(argv[1], "-n") == 0) ++argv, --argc, type = filter_BPF_SPK_N; return lsx_biquad_getopts(effp, argc, argv, 1, 2, 0, 1, 2, "hkqo", type); } static int deemph_getopts(sox_effect_t * effp, int argc, char **argv) { return lsx_biquad_getopts(effp, argc, argv, 0, 0, 0, 1, 2, "s", filter_deemph); } static int riaa_getopts(sox_effect_t * effp, int argc, char **argv) { priv_t * p = (priv_t *)effp->priv; p->filter_type = filter_riaa; (void)argv; return --argc? lsx_usage(effp) : SOX_SUCCESS; } static void make_poly_from_roots( double const * roots, size_t num_roots, double * poly) { size_t i, j; poly[0] = 1; poly[1] = -roots[0]; memset(poly + 2, 0, (num_roots + 1 - 2) * sizeof(*poly)); for (i = 1; i < num_roots; ++i) for (j = num_roots; j > 0; --j) poly[j] -= poly[j - 1] * roots[i]; } static int start(sox_effect_t * effp) { priv_t * p = (priv_t *)effp->priv; double w0, A, alpha, mult; if (p->filter_type == filter_deemph) { /* See deemph.plt for documentation */ if (effp->in_signal.rate == 44100) { p->fc = 5283; p->width = 0.4845; p->gain = -9.477; } else if (effp->in_signal.rate == 48000) { p->fc = 5356; p->width = 0.479; p->gain = -9.62; } else { lsx_fail("sample rate must be 44100 (audio-CD) or 48000 (DAT)"); return SOX_EOF; } } w0 = 2 * M_PI * p->fc / effp->in_signal.rate; A = exp(p->gain / 40 * log(10.)); alpha = 0, mult = dB_to_linear(max(p->gain, 0)); if (w0 > M_PI) { lsx_fail("frequency must be less than half the sample-rate (Nyquist rate)"); return SOX_EOF; } /* Set defaults: */ p->b0 = p->b1 = p->b2 = p->a1 = p->a2 = 0; p->a0 = 1; if (p->width) switch (p->width_type) { case width_slope: alpha = sin(w0)/2 * sqrt((A + 1/A)*(1/p->width - 1) + 2); break; case width_Q: alpha = sin(w0)/(2*p->width); break; case width_bw_oct: alpha = sin(w0)*sinh(log(2.)/2 * p->width * w0/sin(w0)); break; case width_bw_Hz: alpha = sin(w0)/(2*p->fc/p->width); break; case width_bw_kHz: assert(0); /* Shouldn't get here */ case width_bw_old: alpha = tan(M_PI * p->width / effp->in_signal.rate); break; } switch (p->filter_type) { case filter_LPF: /* H(s) = 1 / (s^2 + s/Q + 1) */ p->b0 = (1 - cos(w0))/2; p->b1 = 1 - cos(w0); p->b2 = (1 - cos(w0))/2; p->a0 = 1 + alpha; p->a1 = -2*cos(w0); p->a2 = 1 - alpha; break; case filter_HPF: /* H(s) = s^2 / (s^2 + s/Q + 1) */ p->b0 = (1 + cos(w0))/2; p->b1 = -(1 + cos(w0)); p->b2 = (1 + cos(w0))/2; p->a0 = 1 + alpha; p->a1 = -2*cos(w0); p->a2 = 1 - alpha; break; case filter_BPF_CSG: /* H(s) = s / (s^2 + s/Q + 1) (constant skirt gain, peak gain = Q) */ p->b0 = sin(w0)/2; p->b1 = 0; p->b2 = -sin(w0)/2; p->a0 = 1 + alpha; p->a1 = -2*cos(w0); p->a2 = 1 - alpha; break; case filter_BPF: /* H(s) = (s/Q) / (s^2 + s/Q + 1) (constant 0 dB peak gain) */ p->b0 = alpha; p->b1 = 0; p->b2 = -alpha; p->a0 = 1 + alpha; p->a1 = -2*cos(w0); p->a2 = 1 - alpha; break; case filter_notch: /* H(s) = (s^2 + 1) / (s^2 + s/Q + 1) */ p->b0 = 1; p->b1 = -2*cos(w0); p->b2 = 1; p->a0 = 1 + alpha; p->a1 = -2*cos(w0); p->a2 = 1 - alpha; break; case filter_APF: /* H(s) = (s^2 - s/Q + 1) / (s^2 + s/Q + 1) */ p->b0 = 1 - alpha; p->b1 = -2*cos(w0); p->b2 = 1 + alpha; p->a0 = 1 + alpha; p->a1 = -2*cos(w0); p->a2 = 1 - alpha; break; case filter_peakingEQ: /* H(s) = (s^2 + s*(A/Q) + 1) / (s^2 + s/(A*Q) + 1) */ if (A == 1) return SOX_EFF_NULL; p->b0 = 1 + alpha*A; p->b1 = -2*cos(w0); p->b2 = 1 - alpha*A; p->a0 = 1 + alpha/A; p->a1 = -2*cos(w0); p->a2 = 1 - alpha/A; break; case filter_lowShelf: /* H(s) = A * (s^2 + (sqrt(A)/Q)*s + A)/(A*s^2 + (sqrt(A)/Q)*s + 1) */ if (A == 1) return SOX_EFF_NULL; p->b0 = A*( (A+1) - (A-1)*cos(w0) + 2*sqrt(A)*alpha ); p->b1 = 2*A*( (A-1) - (A+1)*cos(w0) ); p->b2 = A*( (A+1) - (A-1)*cos(w0) - 2*sqrt(A)*alpha ); p->a0 = (A+1) + (A-1)*cos(w0) + 2*sqrt(A)*alpha; p->a1 = -2*( (A-1) + (A+1)*cos(w0) ); p->a2 = (A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha; break; case filter_deemph: /* Falls through to high-shelf... */ case filter_highShelf: /* H(s) = A * (A*s^2 + (sqrt(A)/Q)*s + 1)/(s^2 + (sqrt(A)/Q)*s + A) */ if (!A) return SOX_EFF_NULL; p->b0 = A*( (A+1) + (A-1)*cos(w0) + 2*sqrt(A)*alpha ); p->b1 = -2*A*( (A-1) + (A+1)*cos(w0) ); p->b2 = A*( (A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha ); p->a0 = (A+1) - (A-1)*cos(w0) + 2*sqrt(A)*alpha; p->a1 = 2*( (A-1) - (A+1)*cos(w0) ); p->a2 = (A+1) - (A-1)*cos(w0) - 2*sqrt(A)*alpha; break; case filter_LPF_1: /* single-pole */ p->a1 = -exp(-w0); p->b0 = 1 + p->a1; break; case filter_HPF_1: /* single-pole */ p->a1 = -exp(-w0); p->b0 = (1 - p->a1)/2; p->b1 = -p->b0; break; case filter_BPF_SPK: case filter_BPF_SPK_N: { double bw_Hz; if (!p->width) p->width = p->fc / 2; bw_Hz = p->width_type == width_Q? p->fc / p->width : p->width_type == width_bw_Hz? p->width : p->fc * (pow(2., p->width) - 1) * pow(2., -0.5 * p->width); /* bw_oct */ #include "band.h" /* Has different licence */ break; } case filter_AP1: /* Experimental 1-pole all-pass from Tom Erbe @ UCSD */ p->b0 = exp(-w0); p->b1 = -1; p->a1 = -exp(-w0); break; case filter_AP2: /* Experimental 2-pole all-pass from Tom Erbe @ UCSD */ p->b0 = 1 - sin(w0); p->b1 = -2 * cos(w0); p->b2 = 1 + sin(w0); p->a0 = 1 + sin(w0); p->a1 = -2 * cos(w0); p->a2 = 1 - sin(w0); break; case filter_riaa: /* http://www.dsprelated.com/showmessage/73300/3.php */ if (effp->in_signal.rate == 44100) { static const double zeros[] = {-0.2014898, 0.9233820}; static const double poles[] = {0.7083149, 0.9924091}; make_poly_from_roots(zeros, (size_t)2, &p->b0); make_poly_from_roots(poles, (size_t)2, &p->a0); } else if (effp->in_signal.rate == 48000) { static const double zeros[] = {-0.1766069, 0.9321590}; static const double poles[] = {0.7396325, 0.9931330}; make_poly_from_roots(zeros, (size_t)2, &p->b0); make_poly_from_roots(poles, (size_t)2, &p->a0); } else if (effp->in_signal.rate == 88200) { static const double zeros[] = {-0.1168735, 0.9648312}; static const double poles[] = {0.8590646, 0.9964002}; make_poly_from_roots(zeros, (size_t)2, &p->b0); make_poly_from_roots(poles, (size_t)2, &p->a0); } else if (effp->in_signal.rate == 96000) { static const double zeros[] = {-0.1141486, 0.9676817}; static const double poles[] = {0.8699137, 0.9966946}; make_poly_from_roots(zeros, (size_t)2, &p->b0); make_poly_from_roots(poles, (size_t)2, &p->a0); } else if (effp->in_signal.rate == 192000) { static const double zeros[] = {-0.1040610965, 0.9837523263}; static const double poles[] = {0.9328992971, 0.9983633125}; make_poly_from_roots(zeros, (size_t)2, &p->b0); make_poly_from_roots(poles, (size_t)2, &p->a0); } else { lsx_fail("Sample rate must be 44.1k, 48k, 88.2k, 96k, or 192k"); return SOX_EOF; } { /* Normalise to 0dB at 1kHz (Thanks to Glenn Davis) */ double y = 2 * M_PI * 1000 / effp->in_signal.rate; double b_re = p->b0 + p->b1 * cos(-y) + p->b2 * cos(-2 * y); double a_re = p->a0 + p->a1 * cos(-y) + p->a2 * cos(-2 * y); double b_im = p->b1 * sin(-y) + p->b2 * sin(-2 * y); double a_im = p->a1 * sin(-y) + p->a2 * sin(-2 * y); double g = 1 / sqrt((sqr(b_re) + sqr(b_im)) / (sqr(a_re) + sqr(a_im))); p->b0 *= g; p->b1 *= g; p->b2 *= g; } mult = (p->b0 + p->b1 + p->b2) / (p->a0 + p->a1 + p->a2); lsx_debug("gain=%f", linear_to_dB(mult)); break; } if (effp->in_signal.mult) *effp->in_signal.mult /= mult; return lsx_biquad_start(effp); } #define BIQUAD_EFFECT(name,group,usage,flags) \ sox_effect_handler_t const * lsx_##name##_effect_fn(void) { \ static sox_effect_handler_t handler = { \ #name, usage, flags, \ group##_getopts, start, lsx_biquad_flow, 0, 0, 0, sizeof(biquad_t)\ }; \ return &handler; \ } BIQUAD_EFFECT(highpass, hilo2, "[-1|-2] frequency [width[q|o|h|k](0.707q)]", 0) BIQUAD_EFFECT(lowpass, hilo2, "[-1|-2] frequency [width[q|o|h|k]](0.707q)", 0) BIQUAD_EFFECT(bandpass, bandpass, "[-c] frequency width[h|k|q|o]", 0) BIQUAD_EFFECT(bandreject,bandrej, "frequency width[h|k|q|o]", 0) BIQUAD_EFFECT(allpass, allpass, "frequency width[h|k|q|o]", 0) BIQUAD_EFFECT(bass, tone, "gain [frequency(100) [width[s|h|k|q|o]](0.5s)]", 0) BIQUAD_EFFECT(treble, tone, "gain [frequency(3000) [width[s|h|k|q|o]](0.5s)]", 0) BIQUAD_EFFECT(equalizer, equalizer,"frequency width[q|o|h|k] gain", 0) BIQUAD_EFFECT(band, band, "[-n] center [width[h|k|q|o]]", 0) BIQUAD_EFFECT(deemph, deemph, NULL, 0) BIQUAD_EFFECT(riaa, riaa, NULL, 0)