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   1 /*
   2  * IIR filter
   3  * Copyright (c) 2008 Konstantin Shishkov
   4  *
   5  * This file is part of Libav.
   6  *
   7  * Libav is free software; you can redistribute it and/or
   8  * modify it under the terms of the GNU Lesser General Public
   9  * License as published by the Free Software Foundation; either
  10  * version 2.1 of the License, or (at your option) any later version.
  11  *
  12  * Libav is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15  * Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public
  18  * License along with Libav; if not, write to the Free Software
  19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  20  */
  21
  22 /**
  23  * @file
  24  * different IIR filters implementation
  25  */
  26
  27 #include <math.h>
  28
  29 #include "libavutil/attributes.h"
  30 #include "libavutil/common.h"
  31 #include "libavutil/log.h"
  32
  33 #include "iirfilter.h"
  34
  35 /**
  36  * IIR filter global parameters
  37  */
  38 typedef struct FFIIRFilterCoeffs {
  39     int   order;
  40     float gain;
  41     int   *cx;
  42     float *cy;
  43 } FFIIRFilterCoeffs;
  44
  45 /**
  46  * IIR filter state
  47  */
  48 typedef struct FFIIRFilterState {
  49     float x[1];
  50 } FFIIRFilterState;
  51
  52 /// maximum supported filter order
  53 #define MAXORDER 30
  54
  55 static av_cold int butterworth_init_coeffs(void *avc,
  56                                            struct FFIIRFilterCoeffs *c,
  57                                            enum IIRFilterMode filt_mode,
  58                                            int order, float cutoff_ratio,
  59                                            float stopband)
  60 {
  61     int i, j;
  62     double wa;
  63     double p[MAXORDER + 1][2];
  64
  65     if (filt_mode != FF_FILTER_MODE_LOWPASS) {
  66         av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
  67                                   "low-pass filter mode\n");
  68         return -1;
  69     }
  70     if (order & 1) {
  71         av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
  72                                   "even filter orders\n");
  73         return -1;
  74     }
  75
  76     wa = 2 * tan(M_PI * 0.5 * cutoff_ratio);
  77
  78     c->cx[0] = 1;
  79     for (i = 1; i < (order >> 1) + 1; i++)
  80         c->cx[i] = c->cx[i - 1] * (order - i + 1LL) / i;
  81
  82     p[0][0] = 1.0;
  83     p[0][1] = 0.0;
  84     for (i = 1; i <= order; i++)
  85         p[i][0] = p[i][1] = 0.0;
  86     for (i = 0; i < order; i++) {
  87         double zp[2];
  88         double th = (i + (order >> 1) + 0.5) * M_PI / order;
  89         double a_re, a_im, c_re, c_im;
  90         zp[0] = cos(th) * wa;
  91         zp[1] = sin(th) * wa;
  92         a_re  = zp[0] + 2.0;
  93         c_re  = zp[0] - 2.0;
  94         a_im  =
  95         c_im  = zp[1];
  96         zp[0] = (a_re * c_re + a_im * c_im) / (c_re * c_re + c_im * c_im);
  97         zp[1] = (a_im * c_re - a_re * c_im) / (c_re * c_re + c_im * c_im);
  98
  99         for (j = order; j >= 1; j--) {
 100             a_re    = p[j][0];
 101             a_im    = p[j][1];
 102             p[j][0] = a_re * zp[0] - a_im * zp[1] + p[j - 1][0];
 103             p[j][1] = a_re * zp[1] + a_im * zp[0] + p[j - 1][1];
 104         }
 105         a_re    = p[0][0] * zp[0] - p[0][1] * zp[1];
 106         p[0][1] = p[0][0] * zp[1] + p[0][1] * zp[0];
 107         p[0][0] = a_re;
 108     }
 109     c->gain = p[order][0];
 110     for (i = 0; i < order; i++) {
 111         c->gain += p[i][0];
 112         c->cy[i] = (-p[i][0] * p[order][0] + -p[i][1] * p[order][1]) /
 113                    (p[order][0] * p[order][0] + p[order][1] * p[order][1]);
 114     }
 115     c->gain /= 1 << order;
 116
 117     return 0;
 118 }
 119
 120 static av_cold int biquad_init_coeffs(void *avc, struct FFIIRFilterCoeffs *c,
 121                                       enum IIRFilterMode filt_mode, int order,
 122                                       float cutoff_ratio, float stopband)
 123 {
 124     double cos_w0, sin_w0;
 125     double a0, x0, x1;
 126
 127     if (filt_mode != FF_FILTER_MODE_HIGHPASS &&
 128         filt_mode != FF_FILTER_MODE_LOWPASS) {
 129         av_log(avc, AV_LOG_ERROR, "Biquad filter currently only supports "
 130                                   "high-pass and low-pass filter modes\n");
 131         return -1;
 132     }
 133     if (order != 2) {
 134         av_log(avc, AV_LOG_ERROR, "Biquad filter must have order of 2\n");
 135         return -1;
 136     }
 137
 138     cos_w0 = cos(M_PI * cutoff_ratio);
 139     sin_w0 = sin(M_PI * cutoff_ratio);
 140
 141     a0 = 1.0 + (sin_w0 / 2.0);
 142
 143     if (filt_mode == FF_FILTER_MODE_HIGHPASS) {
 144         c->gain  =  ((1.0 + cos_w0) / 2.0)  / a0;
 145         x0       =  ((1.0 + cos_w0) / 2.0)  / a0;
 146         x1       = (-(1.0 + cos_w0))        / a0;
 147     } else { // FF_FILTER_MODE_LOWPASS
 148         c->gain  =  ((1.0 - cos_w0) / 2.0)  / a0;
 149         x0       =  ((1.0 - cos_w0) / 2.0)  / a0;
 150         x1       =   (1.0 - cos_w0)         / a0;
 151     }
 152     c->cy[0] = (-1.0 + (sin_w0 / 2.0)) / a0;
 153     c->cy[1] =  (2.0 *  cos_w0)        / a0;
 154
 155     // divide by gain to make the x coeffs integers.
 156     // during filtering, the delay state will include the gain multiplication
 157     c->cx[0] = lrintf(x0 / c->gain);
 158     c->cx[1] = lrintf(x1 / c->gain);
 159
 160     return 0;
 161 }
 162
 163 av_cold struct FFIIRFilterCoeffs *ff_iir_filter_init_coeffs(void *avc,
 164                                                             enum IIRFilterType filt_type,
 165                                                             enum IIRFilterMode filt_mode,
 166                                                             int order, float cutoff_ratio,
 167                                                             float stopband, float ripple)
 168 {
 169     FFIIRFilterCoeffs *c;
 170     int ret = 0;
 171
 172     if (order <= 0 || order > MAXORDER || cutoff_ratio >= 1.0)
 173         return NULL;
 174
 175     FF_ALLOCZ_OR_GOTO(avc, c, sizeof(FFIIRFilterCoeffs),
 176                       init_fail);
 177     FF_ALLOC_OR_GOTO(avc, c->cx, sizeof(c->cx[0]) * ((order >> 1) + 1),
 178                      init_fail);
 179     FF_ALLOC_OR_GOTO(avc, c->cy, sizeof(c->cy[0]) * order,
 180                      init_fail);
 181     c->order = order;
 182
 183     switch (filt_type) {
 184     case FF_FILTER_TYPE_BUTTERWORTH:
 185         ret = butterworth_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
 186                                       stopband);
 187         break;
 188     case FF_FILTER_TYPE_BIQUAD:
 189         ret = biquad_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
 190                                  stopband);
 191         break;
 192     default:
 193         av_log(avc, AV_LOG_ERROR, "filter type is not currently implemented\n");
 194         goto init_fail;
 195     }
 196
 197     if (!ret)
 198         return c;
 199
 200 init_fail:
 201     ff_iir_filter_free_coeffs(c);
 202     return NULL;
 203 }
 204
 205 av_cold struct FFIIRFilterState *ff_iir_filter_init_state(int order)
 206 {
 207     FFIIRFilterState *s = av_mallocz(sizeof(FFIIRFilterState) + sizeof(s->x[0]) * (order - 1));
 208     return s;
 209 }
 210
 211 #define CONV_S16(dest, source) dest = av_clip_int16(lrintf(source));
 212
 213 #define CONV_FLT(dest, source) dest = source;
 214
 215 #define FILTER_BW_O4_1(i0, i1, i2, i3, fmt)             \
 216     in = *src0    * c->gain  +                          \
 217          c->cy[0] * s->x[i0] +                          \
 218          c->cy[1] * s->x[i1] +                          \
 219          c->cy[2] * s->x[i2] +                          \
 220          c->cy[3] * s->x[i3];                           \
 221     res = (s->x[i0] + in)       * 1 +                   \
 222           (s->x[i1] + s->x[i3]) * 4 +                   \
 223            s->x[i2]             * 6;                    \
 224     CONV_ ## fmt(*dst0, res)                            \
 225     s->x[i0] = in;                                      \
 226     src0    += sstep;                                   \
 227     dst0    += dstep;
 228
 229 #define FILTER_BW_O4(type, fmt) {           \
 230     int i;                                  \
 231     const type *src0 = src;                 \
 232     type       *dst0 = dst;                 \
 233     for (i = 0; i < size; i += 4) {         \
 234         float in, res;                      \
 235         FILTER_BW_O4_1(0, 1, 2, 3, fmt);    \
 236         FILTER_BW_O4_1(1, 2, 3, 0, fmt);    \
 237         FILTER_BW_O4_1(2, 3, 0, 1, fmt);    \
 238         FILTER_BW_O4_1(3, 0, 1, 2, fmt);    \
 239     }                                       \
 240 }
 241
 242 #define FILTER_DIRECT_FORM_II(type, fmt) {                                  \
 243     int i;                                                                  \
 244     const type *src0 = src;                                                 \
 245     type       *dst0 = dst;                                                 \
 246     for (i = 0; i < size; i++) {                                            \
 247         int j;                                                              \
 248         float in, res;                                                      \
 249         in = *src0 * c->gain;                                               \
 250         for (j = 0; j < c->order; j++)                                      \
 251             in += c->cy[j] * s->x[j];                                       \
 252         res = s->x[0] + in + s->x[c->order >> 1] * c->cx[c->order >> 1];    \
 253         for (j = 1; j < c->order >> 1; j++)                                 \
 254             res += (s->x[j] + s->x[c->order - j]) * c->cx[j];               \
 255         for (j = 0; j < c->order - 1; j++)                                  \
 256             s->x[j] = s->x[j + 1];                                          \
 257         CONV_ ## fmt(*dst0, res)                                            \
 258         s->x[c->order - 1] = in;                                            \
 259         src0              += sstep;                                         \
 260         dst0              += dstep;                                         \
 261     }                                                                       \
 262 }
 263
 264 #define FILTER_O2(type, fmt) {                                              \
 265     int i;                                                                  \
 266     const type *src0 = src;                                                 \
 267     type       *dst0 = dst;                                                 \
 268     for (i = 0; i < size; i++) {                                            \
 269         float in = *src0   * c->gain  +                                     \
 270                    s->x[0] * c->cy[0] +                                     \
 271                    s->x[1] * c->cy[1];                                      \
 272         CONV_ ## fmt(*dst0, s->x[0] + in + s->x[1] * c->cx[1])              \
 273         s->x[0] = s->x[1];                                                  \
 274         s->x[1] = in;                                                       \
 275         src0   += sstep;                                                    \
 276         dst0   += dstep;                                                    \
 277     }                                                                       \
 278 }
 279
 280 void ff_iir_filter(const struct FFIIRFilterCoeffs *c,
 281                    struct FFIIRFilterState *s, int size,
 282                    const int16_t *src, ptrdiff_t sstep,
 283                    int16_t *dst, ptrdiff_t dstep)
 284 {
 285     if (c->order == 2) {
 286         FILTER_O2(int16_t, S16)
 287     } else if (c->order == 4) {
 288         FILTER_BW_O4(int16_t, S16)
 289     } else {
 290         FILTER_DIRECT_FORM_II(int16_t, S16)
 291     }
 292 }
 293
 294 void ff_iir_filter_flt(const struct FFIIRFilterCoeffs *c,
 295                        struct FFIIRFilterState *s, int size,
 296                        const float *src, ptrdiff_t sstep,
 297                        float *dst, ptrdiff_t dstep)
 298 {
 299     if (c->order == 2) {
 300         FILTER_O2(float, FLT)
 301     } else if (c->order == 4) {
 302         FILTER_BW_O4(float, FLT)
 303     } else {
 304         FILTER_DIRECT_FORM_II(float, FLT)
 305     }
 306 }
 307
 308 av_cold void ff_iir_filter_free_state(struct FFIIRFilterState *state)
 309 {
 310     av_free(state);
 311 }
 312
 313 av_cold void ff_iir_filter_free_coeffs(struct FFIIRFilterCoeffs *coeffs)
 314 {
 315     if (coeffs) {
 316         av_free(coeffs->cx);
 317         av_free(coeffs->cy);
 318     }
 319     av_free(coeffs);
 320 }