iirfilter.c
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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 
27 #include "iirfilter.h"
28 #include <math.h>
29 
33 typedef struct FFIIRFilterCoeffs{
34  int order;
35  float gain;
36  int *cx;
37  float *cy;
39 
43 typedef struct FFIIRFilterState{
44  float x[1];
46 
48 #define MAXORDER 30
49 
50 static int butterworth_init_coeffs(void *avc, struct FFIIRFilterCoeffs *c,
51  enum IIRFilterMode filt_mode,
52  int order, float cutoff_ratio,
53  float stopband)
54 {
55  int i, j;
56  double wa;
57  double p[MAXORDER + 1][2];
58 
59  if (filt_mode != FF_FILTER_MODE_LOWPASS) {
60  av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
61  "low-pass filter mode\n");
62  return -1;
63  }
64  if (order & 1) {
65  av_log(avc, AV_LOG_ERROR, "Butterworth filter currently only supports "
66  "even filter orders\n");
67  return -1;
68  }
69 
70  wa = 2 * tan(M_PI * 0.5 * cutoff_ratio);
71 
72  c->cx[0] = 1;
73  for(i = 1; i < (order >> 1) + 1; i++)
74  c->cx[i] = c->cx[i - 1] * (order - i + 1LL) / i;
75 
76  p[0][0] = 1.0;
77  p[0][1] = 0.0;
78  for(i = 1; i <= order; i++)
79  p[i][0] = p[i][1] = 0.0;
80  for(i = 0; i < order; i++){
81  double zp[2];
82  double th = (i + (order >> 1) + 0.5) * M_PI / order;
83  double a_re, a_im, c_re, c_im;
84  zp[0] = cos(th) * wa;
85  zp[1] = sin(th) * wa;
86  a_re = zp[0] + 2.0;
87  c_re = zp[0] - 2.0;
88  a_im =
89  c_im = zp[1];
90  zp[0] = (a_re * c_re + a_im * c_im) / (c_re * c_re + c_im * c_im);
91  zp[1] = (a_im * c_re - a_re * c_im) / (c_re * c_re + c_im * c_im);
92 
93  for(j = order; j >= 1; j--)
94  {
95  a_re = p[j][0];
96  a_im = p[j][1];
97  p[j][0] = a_re*zp[0] - a_im*zp[1] + p[j-1][0];
98  p[j][1] = a_re*zp[1] + a_im*zp[0] + p[j-1][1];
99  }
100  a_re = p[0][0]*zp[0] - p[0][1]*zp[1];
101  p[0][1] = p[0][0]*zp[1] + p[0][1]*zp[0];
102  p[0][0] = a_re;
103  }
104  c->gain = p[order][0];
105  for(i = 0; i < order; i++){
106  c->gain += p[i][0];
107  c->cy[i] = (-p[i][0] * p[order][0] + -p[i][1] * p[order][1]) /
108  (p[order][0] * p[order][0] + p[order][1] * p[order][1]);
109  }
110  c->gain /= 1 << order;
111 
112  return 0;
113 }
114 
115 static int biquad_init_coeffs(void *avc, struct FFIIRFilterCoeffs *c,
116  enum IIRFilterMode filt_mode, int order,
117  float cutoff_ratio, float stopband)
118 {
119  double cos_w0, sin_w0;
120  double a0, x0, x1;
121 
122  if (filt_mode != FF_FILTER_MODE_HIGHPASS &&
123  filt_mode != FF_FILTER_MODE_LOWPASS) {
124  av_log(avc, AV_LOG_ERROR, "Biquad filter currently only supports "
125  "high-pass and low-pass filter modes\n");
126  return -1;
127  }
128  if (order != 2) {
129  av_log(avc, AV_LOG_ERROR, "Biquad filter must have order of 2\n");
130  return -1;
131  }
132 
133  cos_w0 = cos(M_PI * cutoff_ratio);
134  sin_w0 = sin(M_PI * cutoff_ratio);
135 
136  a0 = 1.0 + (sin_w0 / 2.0);
137 
138  if (filt_mode == FF_FILTER_MODE_HIGHPASS) {
139  c->gain = ((1.0 + cos_w0) / 2.0) / a0;
140  x0 = ((1.0 + cos_w0) / 2.0) / a0;
141  x1 = (-(1.0 + cos_w0)) / a0;
142  } else { // FF_FILTER_MODE_LOWPASS
143  c->gain = ((1.0 - cos_w0) / 2.0) / a0;
144  x0 = ((1.0 - cos_w0) / 2.0) / a0;
145  x1 = (1.0 - cos_w0) / a0;
146  }
147  c->cy[0] = (-1.0 + (sin_w0 / 2.0)) / a0;
148  c->cy[1] = (2.0 * cos_w0) / a0;
149 
150  // divide by gain to make the x coeffs integers.
151  // during filtering, the delay state will include the gain multiplication
152  c->cx[0] = lrintf(x0 / c->gain);
153  c->cx[1] = lrintf(x1 / c->gain);
154 
155  return 0;
156 }
157 
159  enum IIRFilterType filt_type,
160  enum IIRFilterMode filt_mode,
161  int order, float cutoff_ratio,
162  float stopband, float ripple)
163 {
165  int ret = 0;
166 
167  if (order <= 0 || order > MAXORDER || cutoff_ratio >= 1.0)
168  return NULL;
169 
170  FF_ALLOCZ_OR_GOTO(avc, c, sizeof(FFIIRFilterCoeffs),
171  init_fail);
172  FF_ALLOC_OR_GOTO (avc, c->cx, sizeof(c->cx[0]) * ((order >> 1) + 1),
173  init_fail);
174  FF_ALLOC_OR_GOTO (avc, c->cy, sizeof(c->cy[0]) * order,
175  init_fail);
176  c->order = order;
177 
178  switch (filt_type) {
180  ret = butterworth_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
181  stopband);
182  break;
184  ret = biquad_init_coeffs(avc, c, filt_mode, order, cutoff_ratio,
185  stopband);
186  break;
187  default:
188  av_log(avc, AV_LOG_ERROR, "filter type is not currently implemented\n");
189  goto init_fail;
190  }
191 
192  if (!ret)
193  return c;
194 
195 init_fail:
197  return NULL;
198 }
199 
201 {
202  FFIIRFilterState* s = av_mallocz(sizeof(FFIIRFilterState) + sizeof(s->x[0]) * (order - 1));
203  return s;
204 }
205 
206 #define CONV_S16(dest, source) dest = av_clip_int16(lrintf(source));
207 
208 #define CONV_FLT(dest, source) dest = source;
209 
210 #define FILTER_BW_O4_1(i0, i1, i2, i3, fmt) \
211  in = *src0 * c->gain \
212  + c->cy[0]*s->x[i0] + c->cy[1]*s->x[i1] \
213  + c->cy[2]*s->x[i2] + c->cy[3]*s->x[i3]; \
214  res = (s->x[i0] + in )*1 \
215  + (s->x[i1] + s->x[i3])*4 \
216  + s->x[i2] *6; \
217  CONV_##fmt(*dst0, res) \
218  s->x[i0] = in; \
219  src0 += sstep; \
220  dst0 += dstep;
221 
222 #define FILTER_BW_O4(type, fmt) { \
223  int i; \
224  const type *src0 = src; \
225  type *dst0 = dst; \
226  for (i = 0; i < size; i += 4) { \
227  float in, res; \
228  FILTER_BW_O4_1(0, 1, 2, 3, fmt); \
229  FILTER_BW_O4_1(1, 2, 3, 0, fmt); \
230  FILTER_BW_O4_1(2, 3, 0, 1, fmt); \
231  FILTER_BW_O4_1(3, 0, 1, 2, fmt); \
232  } \
233 }
234 
235 #define FILTER_DIRECT_FORM_II(type, fmt) { \
236  int i; \
237  const type *src0 = src; \
238  type *dst0 = dst; \
239  for (i = 0; i < size; i++) { \
240  int j; \
241  float in, res; \
242  in = *src0 * c->gain; \
243  for(j = 0; j < c->order; j++) \
244  in += c->cy[j] * s->x[j]; \
245  res = s->x[0] + in + s->x[c->order >> 1] * c->cx[c->order >> 1]; \
246  for(j = 1; j < c->order >> 1; j++) \
247  res += (s->x[j] + s->x[c->order - j]) * c->cx[j]; \
248  for(j = 0; j < c->order - 1; j++) \
249  s->x[j] = s->x[j + 1]; \
250  CONV_##fmt(*dst0, res) \
251  s->x[c->order - 1] = in; \
252  src0 += sstep; \
253  dst0 += dstep; \
254  } \
255 }
256 
257 #define FILTER_O2(type, fmt) { \
258  int i; \
259  const type *src0 = src; \
260  type *dst0 = dst; \
261  for (i = 0; i < size; i++) { \
262  float in = *src0 * c->gain + \
263  s->x[0] * c->cy[0] + \
264  s->x[1] * c->cy[1]; \
265  CONV_##fmt(*dst0, s->x[0] + in + s->x[1] * c->cx[1]) \
266  s->x[0] = s->x[1]; \
267  s->x[1] = in; \
268  src0 += sstep; \
269  dst0 += dstep; \
270  } \
271 }
272 
273 void ff_iir_filter(const struct FFIIRFilterCoeffs *c,
274  struct FFIIRFilterState *s, int size,
275  const int16_t *src, int sstep, int16_t *dst, int dstep)
276 {
277  if (c->order == 2) {
278  FILTER_O2(int16_t, S16)
279  } else if (c->order == 4) {
280  FILTER_BW_O4(int16_t, S16)
281  } else {
282  FILTER_DIRECT_FORM_II(int16_t, S16)
283  }
284 }
285 
287  struct FFIIRFilterState *s, int size,
288  const float *src, int sstep, float *dst, int dstep)
289 {
290  if (c->order == 2) {
291  FILTER_O2(float, FLT)
292  } else if (c->order == 4) {
293  FILTER_BW_O4(float, FLT)
294  } else {
295  FILTER_DIRECT_FORM_II(float, FLT)
296  }
297 }
298 
300 {
301  av_free(state);
302 }
303 
305 {
306  if(coeffs){
307  av_free(coeffs->cx);
308  av_free(coeffs->cy);
309  }
310  av_free(coeffs);
311 }
312 
313 #ifdef TEST
314 #undef printf
315 #include <stdio.h>
316 
317 #define FILT_ORDER 4
318 #define SIZE 1024
319 int main(void)
320 {
321  struct FFIIRFilterCoeffs *fcoeffs = NULL;
322  struct FFIIRFilterState *fstate = NULL;
323  float cutoff_coeff = 0.4;
324  int16_t x[SIZE], y[SIZE];
325  int i;
326 
329  cutoff_coeff, 0.0, 0.0);
331 
332  for (i = 0; i < SIZE; i++) {
333  x[i] = lrint(0.75 * INT16_MAX * sin(0.5*M_PI*i*i/SIZE));
334  }
335 
336  ff_iir_filter(fcoeffs, fstate, SIZE, x, 1, y, 1);
337 
338  for (i = 0; i < SIZE; i++)
339  printf("%6d %6d\n", x[i], y[i]);
340 
341  ff_iir_filter_free_coeffs(fcoeffs);
342  ff_iir_filter_free_state(fstate);
343  return 0;
344 }
345 #endif /* TEST */