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   1 /*
   2  * IIR filter
   3  * Copyright (c) 2008 Konstantin Shishkov
   4  *
   5  * This file is part of FFmpeg.
   6  *
   7  * FFmpeg 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  * FFmpeg 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 FFmpeg; 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/attributes.h"
  30 #include "libavutil/common.h"
  31
  32 /**
  33  * IIR filter global parameters
  34  */
  35 typedef struct FFIIRFilterCoeffs{
  36     int   order;
  37     float gain;
  38     int   *cx;
  39     float *cy;
  40 }FFIIRFilterCoeffs;
  41
  42 /**
  43  * IIR filter state
  44  */
  45 typedef struct FFIIRFilterState{
  46     float x[1];
  47 }FFIIRFilterState;
  48
  49 /// maximum supported filter order
  50 #define MAXORDER 30
  51
  52 static av_cold int butterworth_init_coeffs(void *avc,
  53                                            struct FFIIRFilterCoeffs *c,
  54                                            enum IIRFilterMode filt_mode,
  55                                            int order, float cutoff_ratio,
  56                                            float stopband)
  57 {
  58     int i, j;
  59     double wa;
  60     double p[MAXORDER + 1][2];
  61
  62     if (filt_mode != FF_FILTER_MODE_LOWPASS) {
  63         av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
  64                "low-pass filter mode\n");
  65         return -1;
  66     }
  67     if (order & 1) {
  68         av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
  69                "even filter orders\n");
  70         return -1;
  71     }
  72
  73     wa = 2 * tan(M_PI * 0.5 * cutoff_ratio);
  74
  75     c->cx[0] = 1;
  76     for(i = 1; i < (order >> 1) + 1; i++)
  77         c->cx[i] = c->cx[i - 1] * (order - i + 1LL) / i;
  78
  79     p[0][0] = 1.0;
  80     p[0][1] = 0.0;
  81     for(i = 1; i <= order; i++)
  82         p[i][0] = p[i][1] = 0.0;
  83     for(i = 0; i < order; i++){
  84         double zp[2];
  85         double th = (i + (order >> 1) + 0.5) * M_PI / order;
  86         double a_re, a_im, c_re, c_im;
  87         zp[0] = cos(th) * wa;
  88         zp[1] = sin(th) * wa;
  89         a_re = zp[0] + 2.0;
  90         c_re = zp[0] - 2.0;
  91         a_im =
  92         c_im = zp[1];
  93         zp[0] = (a_re * c_re + a_im * c_im) / (c_re * c_re + c_im * c_im);
  94         zp[1] = (a_im * c_re - a_re * c_im) / (c_re * c_re + c_im * c_im);
  95
  96         for(j = order; j >= 1; j--)
  97         {
  98             a_re = p[j][0];
  99             a_im = p[j][1];
 100             p[j][0] = a_re*zp[0] - a_im*zp[1] + p[j-1][0];
 101             p[j][1] = a_re*zp[1] + a_im*zp[0] + p[j-1][1];
 102         }
 103         a_re    = p[0][0]*zp[0] - p[0][1]*zp[1];
 104         p[0][1] = p[0][0]*zp[1] + p[0][1]*zp[0];
 105         p[0][0] = a_re;
 106     }
 107     c->gain = p[order][0];
 108     for(i = 0; i < order; i++){
 109         c->gain += p[i][0];
 110         c->cy[i] = (-p[i][0] * p[order][0] + -p[i][1] * p[order][1]) /
 111                    (p[order][0] * p[order][0] + p[order][1] * p[order][1]);
 112     }
 113     c->gain /= 1 << order;
 114
 115     return 0;
 116 }
 117
 118 static av_cold int biquad_init_coeffs(void *avc, struct FFIIRFilterCoeffs *c,
 119                                       enum IIRFilterMode filt_mode, int order,
 120                                       float cutoff_ratio, float stopband)
 121 {
 122     double cos_w0, sin_w0;
 123     double a0, x0, x1;
 124
 125     if (filt_mode != FF_FILTER_MODE_HIGHPASS &&
 126         filt_mode != FF_FILTER_MODE_LOWPASS) {
 127         av_log(avc, AV_LOG_ERROR, "Biquad filter currently only supports "
 128                "high-pass and low-pass filter modes\n");
 129         return -1;
 130     }
 131     if (order != 2) {
 132         av_log(avc, AV_LOG_ERROR, "Biquad filter must have order of 2\n");
 133         return -1;
 134     }
 135
 136     cos_w0 = cos(M_PI * cutoff_ratio);
 137     sin_w0 = sin(M_PI * cutoff_ratio);
 138
 139     a0 = 1.0 + (sin_w0 / 2.0);
 140
 141     if (filt_mode == FF_FILTER_MODE_HIGHPASS) {
 142         c->gain  =  ((1.0 + cos_w0) / 2.0)  / a0;
 143         x0       =  ((1.0 + cos_w0) / 2.0)  / a0;
 144         x1       = (-(1.0 + cos_w0))        / a0;
 145     } else { // FF_FILTER_MODE_LOWPASS
 146         c->gain  =  ((1.0 - cos_w0) / 2.0)  / a0;
 147         x0       =  ((1.0 - cos_w0) / 2.0)  / a0;
 148         x1       =   (1.0 - cos_w0)         / a0;
 149     }
 150     c->cy[0] = (-1.0 + (sin_w0 / 2.0)) / a0;
 151     c->cy[1] =  (2.0 *  cos_w0)        / a0;
 152
 153     // divide by gain to make the x coeffs integers.
 154     // during filtering, the delay state will include the gain multiplication
 155     c->cx[0] = lrintf(x0 / c->gain);
 156     c->cx[1] = lrintf(x1 / c->gain);
 157
 158     return 0;
 159 }
 160
 161 av_cold struct FFIIRFilterCoeffs* ff_iir_filter_init_coeffs(void *avc,
 162                                                 enum IIRFilterType filt_type,
 163                                                 enum IIRFilterMode filt_mode,
 164                                                 int order, float cutoff_ratio,
 165                                                 float stopband, float ripple)
 166 {
 167     FFIIRFilterCoeffs *c;
 168     int ret = 0;
 169
 170     if (order <= 0 || order > MAXORDER || cutoff_ratio >= 1.0)
 171         return NULL;
 172
 173     FF_ALLOCZ_OR_GOTO(avc, c,     sizeof(FFIIRFilterCoeffs),
 174                       init_fail);
 175     FF_ALLOC_OR_GOTO (avc, c->cx, sizeof(c->cx[0]) * ((order >> 1) + 1),
 176                       init_fail);
 177     FF_ALLOC_OR_GOTO (avc, c->cy, sizeof(c->cy[0]) * order,
 178                       init_fail);
 179     c->order = order;
 180
 181     switch (filt_type) {
 182     case FF_FILTER_TYPE_BUTTERWORTH:
 183         ret = butterworth_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
 184                                       stopband);
 185         break;
 186     case FF_FILTER_TYPE_BIQUAD:
 187         ret = biquad_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
 188                                  stopband);
 189         break;
 190     default:
 191         av_log(avc, AV_LOG_ERROR, "filter type is not currently implemented\n");
 192         goto init_fail;
 193     }
 194
 195     if (!ret)
 196         return c;
 197
 198 init_fail:
 199     ff_iir_filter_free_coeffsp(&c);
 200     return NULL;
 201 }
 202
 203 av_cold struct FFIIRFilterState* ff_iir_filter_init_state(int order)
 204 {
 205     FFIIRFilterState* s = av_mallocz(sizeof(FFIIRFilterState) + sizeof(s->x[0]) * (order - 1));
 206     return s;
 207 }
 208
 209 #define CONV_S16(dest, source) dest = av_clip_int16(lrintf(source));
 210
 211 #define CONV_FLT(dest, source) dest = source;
 212
 213 #define FILTER_BW_O4_1(i0, i1, i2, i3, fmt)         \
 214     in = *src0 * c->gain                            \
 215          + c->cy[0]*s->x[i0] + c->cy[1]*s->x[i1]    \
 216          + c->cy[2]*s->x[i2] + c->cy[3]*s->x[i3];   \
 217     res =  (s->x[i0] + in      )*1                  \
 218          + (s->x[i1] + s->x[i3])*4                  \
 219          +  s->x[i2]            *6;                 \
 220     CONV_##fmt(*dst0, res)                          \
 221     s->x[i0] = in;                                  \
 222     src0 += sstep;                                  \
 223     dst0 += dstep;
 224
 225 #define FILTER_BW_O4(type, fmt) {           \
 226     int i;                                  \
 227     const type *src0 = src;                 \
 228     type       *dst0 = dst;                 \
 229     for (i = 0; i < size; i += 4) {         \
 230         float in, res;                      \
 231         FILTER_BW_O4_1(0, 1, 2, 3, fmt);    \
 232         FILTER_BW_O4_1(1, 2, 3, 0, fmt);    \
 233         FILTER_BW_O4_1(2, 3, 0, 1, fmt);    \
 234         FILTER_BW_O4_1(3, 0, 1, 2, fmt);    \
 235     }                                       \
 236 }
 237
 238 #define FILTER_DIRECT_FORM_II(type, fmt) {                                  \
 239     int i;                                                                  \
 240     const type *src0 = src;                                                 \
 241     type       *dst0 = dst;                                                 \
 242     for (i = 0; i < size; i++) {                                            \
 243         int j;                                                              \
 244         float in, res;                                                      \
 245         in = *src0 * c->gain;                                               \
 246         for(j = 0; j < c->order; j++)                                       \
 247             in += c->cy[j] * s->x[j];                                       \
 248         res = s->x[0] + in + s->x[c->order >> 1] * c->cx[c->order >> 1];    \
 249         for(j = 1; j < c->order >> 1; j++)                                  \
 250             res += (s->x[j] + s->x[c->order - j]) * c->cx[j];               \
 251         for(j = 0; j < c->order - 1; j++)                                   \
 252             s->x[j] = s->x[j + 1];                                          \
 253         CONV_##fmt(*dst0, res)                                              \
 254         s->x[c->order - 1] = in;                                            \
 255         src0 += sstep;                                                      \
 256         dst0 += dstep;                                                      \
 257     }                                                                       \
 258 }
 259
 260 #define FILTER_O2(type, fmt) {                                              \
 261     int i;                                                                  \
 262     const type *src0 = src;                                                 \
 263     type       *dst0 = dst;                                                 \
 264     for (i = 0; i < size; i++) {                                            \
 265         float in = *src0   * c->gain  +                                     \
 266                    s->x[0] * c->cy[0] +                                     \
 267                    s->x[1] * c->cy[1];                                      \
 268         CONV_##fmt(*dst0, s->x[0] + in + s->x[1] * c->cx[1])                \
 269         s->x[0] = s->x[1];                                                  \
 270         s->x[1] = in;                                                       \
 271         src0 += sstep;                                                      \
 272         dst0 += dstep;                                                      \
 273     }                                                                       \
 274 }
 275
 276 void ff_iir_filter(const struct FFIIRFilterCoeffs *c,
 277                    struct FFIIRFilterState *s, int size,
 278                    const int16_t *src, int sstep, int16_t *dst, int dstep)
 279 {
 280     if (c->order == 2) {
 281         FILTER_O2(int16_t, S16)
 282     } else if (c->order == 4) {
 283         FILTER_BW_O4(int16_t, S16)
 284     } else {
 285         FILTER_DIRECT_FORM_II(int16_t, S16)
 286     }
 287 }
 288
 289 void ff_iir_filter_flt(const struct FFIIRFilterCoeffs *c,
 290                        struct FFIIRFilterState *s, int size,
 291                        const float *src, int sstep, float *dst, int dstep)
 292 {
 293     if (c->order == 2) {
 294         FILTER_O2(float, FLT)
 295     } else if (c->order == 4) {
 296         FILTER_BW_O4(float, FLT)
 297     } else {
 298         FILTER_DIRECT_FORM_II(float, FLT)
 299     }
 300 }
 301
 302 av_cold void ff_iir_filter_free_statep(struct FFIIRFilterState **state)
 303 {
 304     av_freep(state);
 305 }
 306
 307 av_cold void ff_iir_filter_free_coeffsp(struct FFIIRFilterCoeffs **coeffsp)
 308 {
 309     struct FFIIRFilterCoeffs *coeffs = *coeffsp;
 310     if(coeffs){
 311         av_freep(&coeffs->cx);
 312         av_freep(&coeffs->cy);
 313     }
 314     av_freep(coeffsp);
 315 }
 316
 317 void ff_iir_filter_init(FFIIRFilterContext *f) {
 318     f->filter_flt = ff_iir_filter_flt;
 319
 320     if (HAVE_MIPSFPU)
 321         ff_iir_filter_init_mips(f);
 322 }
 323
 324 #ifdef TEST
 325 #include <stdio.h>
 326
 327 #define FILT_ORDER 4
 328 #define SIZE 1024
 329 int main(void)
 330 {
 331     struct FFIIRFilterCoeffs *fcoeffs = NULL;
 332     struct FFIIRFilterState  *fstate  = NULL;
 333     float cutoff_coeff = 0.4;
 334     int16_t x[SIZE], y[SIZE];
 335     int i;
 336
 337     fcoeffs = ff_iir_filter_init_coeffs(NULL, FF_FILTER_TYPE_BUTTERWORTH,
 338                                         FF_FILTER_MODE_LOWPASS, FILT_ORDER,
 339                                         cutoff_coeff, 0.0, 0.0);
 340     fstate  = ff_iir_filter_init_state(FILT_ORDER);
 341
 342     for (i = 0; i < SIZE; i++) {
 343         x[i] = lrint(0.75 * INT16_MAX * sin(0.5*M_PI*i*i/SIZE));
 344     }
 345
 346     ff_iir_filter(fcoeffs, fstate, SIZE, x, 1, y, 1);
 347
 348     for (i = 0; i < SIZE; i++)
 349         printf("%6d %6d\n", x[i], y[i]);
 350
 351     ff_iir_filter_free_coeffsp(&fcoeffs);
 352     ff_iir_filter_free_statep(&fstate);
 353     return 0;
 354 }
 355 #endif /* TEST */