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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 "iirfilter.h"
  28 #include <math.h>
  29 #include "libavutil/common.h"
  30
  31 /**
  32  * IIR filter global parameters
  33  */
  34 typedef struct FFIIRFilterCoeffs{
  35     int   order;
  36     float gain;
  37     int   *cx;
  38     float *cy;
  39 }FFIIRFilterCoeffs;
  40
  41 /**
  42  * IIR filter state
  43  */
  44 typedef struct FFIIRFilterState{
  45     float x[1];
  46 }FFIIRFilterState;
  47
  48 /// maximum supported filter order
  49 #define MAXORDER 30
  50
  51 static int butterworth_init_coeffs(void *avc, struct FFIIRFilterCoeffs *c,
  52                                    enum IIRFilterMode filt_mode,
  53                                    int order, float cutoff_ratio,
  54                                    float stopband)
  55 {
  56     int i, j;
  57     double wa;
  58     double p[MAXORDER + 1][2];
  59
  60     if (filt_mode != FF_FILTER_MODE_LOWPASS) {
  61         av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
  62                "low-pass filter mode\n");
  63         return -1;
  64     }
  65     if (order & 1) {
  66         av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
  67                "even filter orders\n");
  68         return -1;
  69     }
  70
  71     wa = 2 * tan(M_PI * 0.5 * cutoff_ratio);
  72
  73     c->cx[0] = 1;
  74     for(i = 1; i < (order >> 1) + 1; i++)
  75         c->cx[i] = c->cx[i - 1] * (order - i + 1LL) / i;
  76
  77     p[0][0] = 1.0;
  78     p[0][1] = 0.0;
  79     for(i = 1; i <= order; i++)
  80         p[i][0] = p[i][1] = 0.0;
  81     for(i = 0; i < order; i++){
  82         double zp[2];
  83         double th = (i + (order >> 1) + 0.5) * M_PI / order;
  84         double a_re, a_im, c_re, c_im;
  85         zp[0] = cos(th) * wa;
  86         zp[1] = sin(th) * wa;
  87         a_re = zp[0] + 2.0;
  88         c_re = zp[0] - 2.0;
  89         a_im =
  90         c_im = zp[1];
  91         zp[0] = (a_re * c_re + a_im * c_im) / (c_re * c_re + c_im * c_im);
  92         zp[1] = (a_im * c_re - a_re * c_im) / (c_re * c_re + c_im * c_im);
  93
  94         for(j = order; j >= 1; j--)
  95         {
  96             a_re = p[j][0];
  97             a_im = p[j][1];
  98             p[j][0] = a_re*zp[0] - a_im*zp[1] + p[j-1][0];
  99             p[j][1] = a_re*zp[1] + a_im*zp[0] + p[j-1][1];
 100         }
 101         a_re    = p[0][0]*zp[0] - p[0][1]*zp[1];
 102         p[0][1] = p[0][0]*zp[1] + p[0][1]*zp[0];
 103         p[0][0] = a_re;
 104     }
 105     c->gain = p[order][0];
 106     for(i = 0; i < order; i++){
 107         c->gain += p[i][0];
 108         c->cy[i] = (-p[i][0] * p[order][0] + -p[i][1] * p[order][1]) /
 109                    (p[order][0] * p[order][0] + p[order][1] * p[order][1]);
 110     }
 111     c->gain /= 1 << order;
 112
 113     return 0;
 114 }
 115
 116 static int biquad_init_coeffs(void *avc, struct FFIIRFilterCoeffs *c,
 117                               enum IIRFilterMode filt_mode, int order,
 118                               float cutoff_ratio, float stopband)
 119 {
 120     double cos_w0, sin_w0;
 121     double a0, x0, x1;
 122
 123     if (filt_mode != FF_FILTER_MODE_HIGHPASS &&
 124         filt_mode != FF_FILTER_MODE_LOWPASS) {
 125         av_log(avc, AV_LOG_ERROR, "Biquad filter currently only supports "
 126                "high-pass and low-pass filter modes\n");
 127         return -1;
 128     }
 129     if (order != 2) {
 130         av_log(avc, AV_LOG_ERROR, "Biquad filter must have order of 2\n");
 131         return -1;
 132     }
 133
 134     cos_w0 = cos(M_PI * cutoff_ratio);
 135     sin_w0 = sin(M_PI * cutoff_ratio);
 136
 137     a0 = 1.0 + (sin_w0 / 2.0);
 138
 139     if (filt_mode == FF_FILTER_MODE_HIGHPASS) {
 140         c->gain  =  ((1.0 + cos_w0) / 2.0)  / a0;
 141         x0       =  ((1.0 + cos_w0) / 2.0)  / a0;
 142         x1       = (-(1.0 + cos_w0))        / a0;
 143     } else { // FF_FILTER_MODE_LOWPASS
 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     }
 148     c->cy[0] = (-1.0 + (sin_w0 / 2.0)) / a0;
 149     c->cy[1] =  (2.0 *  cos_w0)        / a0;
 150
 151     // divide by gain to make the x coeffs integers.
 152     // during filtering, the delay state will include the gain multiplication
 153     c->cx[0] = lrintf(x0 / c->gain);
 154     c->cx[1] = lrintf(x1 / c->gain);
 155
 156     return 0;
 157 }
 158
 159 av_cold struct FFIIRFilterCoeffs* ff_iir_filter_init_coeffs(void *avc,
 160                                                 enum IIRFilterType filt_type,
 161                                                 enum IIRFilterMode filt_mode,
 162                                                 int order, float cutoff_ratio,
 163                                                 float stopband, float ripple)
 164 {
 165     FFIIRFilterCoeffs *c;
 166     int ret = 0;
 167
 168     if (order <= 0 || order > MAXORDER || cutoff_ratio >= 1.0)
 169         return NULL;
 170
 171     FF_ALLOCZ_OR_GOTO(avc, c,     sizeof(FFIIRFilterCoeffs),
 172                       init_fail);
 173     FF_ALLOC_OR_GOTO (avc, c->cx, sizeof(c->cx[0]) * ((order >> 1) + 1),
 174                       init_fail);
 175     FF_ALLOC_OR_GOTO (avc, c->cy, sizeof(c->cy[0]) * order,
 176                       init_fail);
 177     c->order = order;
 178
 179     switch (filt_type) {
 180     case FF_FILTER_TYPE_BUTTERWORTH:
 181         ret = butterworth_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
 182                                       stopband);
 183         break;
 184     case FF_FILTER_TYPE_BIQUAD:
 185         ret = biquad_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
 186                                  stopband);
 187         break;
 188     default:
 189         av_log(avc, AV_LOG_ERROR, "filter type is not currently implemented\n");
 190         goto init_fail;
 191     }
 192
 193     if (!ret)
 194         return c;
 195
 196 init_fail:
 197     ff_iir_filter_free_coeffs(c);
 198     return NULL;
 199 }
 200
 201 av_cold struct FFIIRFilterState* ff_iir_filter_init_state(int order)
 202 {
 203     FFIIRFilterState* s = av_mallocz(sizeof(FFIIRFilterState) + sizeof(s->x[0]) * (order - 1));
 204     return s;
 205 }
 206
 207 #define CONV_S16(dest, source) dest = av_clip_int16(lrintf(source));
 208
 209 #define CONV_FLT(dest, source) dest = source;
 210
 211 #define FILTER_BW_O4_1(i0, i1, i2, i3, fmt)         \
 212     in = *src0 * c->gain                            \
 213          + c->cy[0]*s->x[i0] + c->cy[1]*s->x[i1]    \
 214          + c->cy[2]*s->x[i2] + c->cy[3]*s->x[i3];   \
 215     res =  (s->x[i0] + in      )*1                  \
 216          + (s->x[i1] + s->x[i3])*4                  \
 217          +  s->x[i2]            *6;                 \
 218     CONV_##fmt(*dst0, res)                          \
 219     s->x[i0] = in;                                  \
 220     src0 += sstep;                                  \
 221     dst0 += dstep;
 222
 223 #define FILTER_BW_O4(type, fmt) {           \
 224     int i;                                  \
 225     const type *src0 = src;                 \
 226     type       *dst0 = dst;                 \
 227     for (i = 0; i < size; i += 4) {         \
 228         float in, res;                      \
 229         FILTER_BW_O4_1(0, 1, 2, 3, fmt);    \
 230         FILTER_BW_O4_1(1, 2, 3, 0, fmt);    \
 231         FILTER_BW_O4_1(2, 3, 0, 1, fmt);    \
 232         FILTER_BW_O4_1(3, 0, 1, 2, fmt);    \
 233     }                                       \
 234 }
 235
 236 #define FILTER_DIRECT_FORM_II(type, fmt) {                                  \
 237     int i;                                                                  \
 238     const type *src0 = src;                                                 \
 239     type       *dst0 = dst;                                                 \
 240     for (i = 0; i < size; i++) {                                            \
 241         int j;                                                              \
 242         float in, res;                                                      \
 243         in = *src0 * c->gain;                                               \
 244         for(j = 0; j < c->order; j++)                                       \
 245             in += c->cy[j] * s->x[j];                                       \
 246         res = s->x[0] + in + s->x[c->order >> 1] * c->cx[c->order >> 1];    \
 247         for(j = 1; j < c->order >> 1; j++)                                  \
 248             res += (s->x[j] + s->x[c->order - j]) * c->cx[j];               \
 249         for(j = 0; j < c->order - 1; j++)                                   \
 250             s->x[j] = s->x[j + 1];                                          \
 251         CONV_##fmt(*dst0, res)                                              \
 252         s->x[c->order - 1] = in;                                            \
 253         src0 += sstep;                                                      \
 254         dst0 += dstep;                                                      \
 255     }                                                                       \
 256 }
 257
 258 #define FILTER_O2(type, fmt) {                                              \
 259     int i;                                                                  \
 260     const type *src0 = src;                                                 \
 261     type       *dst0 = dst;                                                 \
 262     for (i = 0; i < size; i++) {                                            \
 263         float in = *src0   * c->gain  +                                     \
 264                    s->x[0] * c->cy[0] +                                     \
 265                    s->x[1] * c->cy[1];                                      \
 266         CONV_##fmt(*dst0, s->x[0] + in + s->x[1] * c->cx[1])                \
 267         s->x[0] = s->x[1];                                                  \
 268         s->x[1] = in;                                                       \
 269         src0 += sstep;                                                      \
 270         dst0 += dstep;                                                      \
 271     }                                                                       \
 272 }
 273
 274 void ff_iir_filter(const struct FFIIRFilterCoeffs *c,
 275                    struct FFIIRFilterState *s, int size,
 276                    const int16_t *src, int sstep, int16_t *dst, int dstep)
 277 {
 278     if (c->order == 2) {
 279         FILTER_O2(int16_t, S16)
 280     } else if (c->order == 4) {
 281         FILTER_BW_O4(int16_t, S16)
 282     } else {
 283         FILTER_DIRECT_FORM_II(int16_t, S16)
 284     }
 285 }
 286
 287 void ff_iir_filter_flt(const struct FFIIRFilterCoeffs *c,
 288                        struct FFIIRFilterState *s, int size,
 289                        const float *src, int sstep, float *dst, int dstep)
 290 {
 291     if (c->order == 2) {
 292         FILTER_O2(float, FLT)
 293     } else if (c->order == 4) {
 294         FILTER_BW_O4(float, FLT)
 295     } else {
 296         FILTER_DIRECT_FORM_II(float, FLT)
 297     }
 298 }
 299
 300 av_cold void ff_iir_filter_free_state(struct FFIIRFilterState *state)
 301 {
 302     av_free(state);
 303 }
 304
 305 av_cold void ff_iir_filter_free_coeffs(struct FFIIRFilterCoeffs *coeffs)
 306 {
 307     if(coeffs){
 308         av_free(coeffs->cx);
 309         av_free(coeffs->cy);
 310     }
 311     av_free(coeffs);
 312 }
 313
 314 #ifdef TEST
 315 #undef printf
 316 #include <stdio.h>
 317
 318 #define FILT_ORDER 4
 319 #define SIZE 1024
 320 int main(void)
 321 {
 322     struct FFIIRFilterCoeffs *fcoeffs = NULL;
 323     struct FFIIRFilterState  *fstate  = NULL;
 324     float cutoff_coeff = 0.4;
 325     int16_t x[SIZE], y[SIZE];
 326     int i;
 327
 328     fcoeffs = ff_iir_filter_init_coeffs(NULL, FF_FILTER_TYPE_BUTTERWORTH,
 329                                         FF_FILTER_MODE_LOWPASS, FILT_ORDER,
 330                                         cutoff_coeff, 0.0, 0.0);
 331     fstate  = ff_iir_filter_init_state(FILT_ORDER);
 332
 333     for (i = 0; i < SIZE; i++) {
 334         x[i] = lrint(0.75 * INT16_MAX * sin(0.5*M_PI*i*i/SIZE));
 335     }
 336
 337     ff_iir_filter(fcoeffs, fstate, SIZE, x, 1, y, 1);
 338
 339     for (i = 0; i < SIZE; i++)
 340         printf("%6d %6d\n", x[i], y[i]);
 341
 342     ff_iir_filter_free_coeffs(fcoeffs);
 343     ff_iir_filter_free_state(fstate);
 344     return 0;
 345 }
 346 #endif /* TEST */