1 /*
2  *  Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
3  *
4  *  Use of this source code is governed by a BSD-style license
5  *  that can be found in the LICENSE file in the root of the source
6  *  tree. An additional intellectual property rights grant can be found
7  *  in the file PATENTS.  All contributing project authors may
8  *  be found in the AUTHORS file in the root of the source tree.
9  */
10 
11 
12 /*
13  * This file contains the function WebRtcSpl_LevinsonDurbin().
14  * The description header can be found in signal_processing_library.h
15  *
16  */
17 
18 #include "signal_processing_library.h"
19 
20 #define SPL_LEVINSON_MAXORDER 20
21 
WebRtcSpl_LevinsonDurbin(WebRtc_Word32 * R,WebRtc_Word16 * A,WebRtc_Word16 * K,WebRtc_Word16 order)22 WebRtc_Word16 WebRtcSpl_LevinsonDurbin(WebRtc_Word32 *R, WebRtc_Word16 *A, WebRtc_Word16 *K,
23                                        WebRtc_Word16 order)
24 {
25     WebRtc_Word16 i, j;
26     // Auto-correlation coefficients in high precision
27     WebRtc_Word16 R_hi[SPL_LEVINSON_MAXORDER + 1], R_low[SPL_LEVINSON_MAXORDER + 1];
28     // LPC coefficients in high precision
29     WebRtc_Word16 A_hi[SPL_LEVINSON_MAXORDER + 1], A_low[SPL_LEVINSON_MAXORDER + 1];
30     // LPC coefficients for next iteration
31     WebRtc_Word16 A_upd_hi[SPL_LEVINSON_MAXORDER + 1], A_upd_low[SPL_LEVINSON_MAXORDER + 1];
32     // Reflection coefficient in high precision
33     WebRtc_Word16 K_hi, K_low;
34     // Prediction gain Alpha in high precision and with scale factor
35     WebRtc_Word16 Alpha_hi, Alpha_low, Alpha_exp;
36     WebRtc_Word16 tmp_hi, tmp_low;
37     WebRtc_Word32 temp1W32, temp2W32, temp3W32;
38     WebRtc_Word16 norm;
39 
40     // Normalize the autocorrelation R[0]...R[order+1]
41 
42     norm = WebRtcSpl_NormW32(R[0]);
43 
44     for (i = order; i >= 0; i--)
45     {
46         temp1W32 = WEBRTC_SPL_LSHIFT_W32(R[i], norm);
47         // Put R in hi and low format
48         R_hi[i] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
49         R_low[i] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
50                 - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)R_hi[i], 16)), 1);
51     }
52 
53     // K = A[1] = -R[1] / R[0]
54 
55     temp2W32 = WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)R_hi[1],16)
56             + WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)R_low[1],1); // R[1] in Q31
57     temp3W32 = WEBRTC_SPL_ABS_W32(temp2W32); // abs R[1]
58     temp1W32 = WebRtcSpl_DivW32HiLow(temp3W32, R_hi[0], R_low[0]); // abs(R[1])/R[0] in Q31
59     // Put back the sign on R[1]
60     if (temp2W32 > 0)
61     {
62         temp1W32 = -temp1W32;
63     }
64 
65     // Put K in hi and low format
66     K_hi = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
67     K_low = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
68             - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)K_hi, 16)), 1);
69 
70     // Store first reflection coefficient
71     K[0] = K_hi;
72 
73     temp1W32 = WEBRTC_SPL_RSHIFT_W32(temp1W32, 4); // A[1] in Q27
74 
75     // Put A[1] in hi and low format
76     A_hi[1] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
77     A_low[1] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
78             - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_hi[1], 16)), 1);
79 
80     // Alpha = R[0] * (1-K^2)
81 
82     temp1W32 = (((WEBRTC_SPL_MUL_16_16(K_hi, K_low) >> 14) + WEBRTC_SPL_MUL_16_16(K_hi, K_hi))
83             << 1); // temp1W32 = k^2 in Q31
84 
85     temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
86     temp1W32 = (WebRtc_Word32)0x7fffffffL - temp1W32; // temp1W32 = (1 - K[0]*K[0]) in Q31
87 
88     // Store temp1W32 = 1 - K[0]*K[0] on hi and low format
89     tmp_hi = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
90     tmp_low = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
91             - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)tmp_hi, 16)), 1);
92 
93     // Calculate Alpha in Q31
94     temp1W32 = ((WEBRTC_SPL_MUL_16_16(R_hi[0], tmp_hi)
95             + (WEBRTC_SPL_MUL_16_16(R_hi[0], tmp_low) >> 15)
96             + (WEBRTC_SPL_MUL_16_16(R_low[0], tmp_hi) >> 15)) << 1);
97 
98     // Normalize Alpha and put it in hi and low format
99 
100     Alpha_exp = WebRtcSpl_NormW32(temp1W32);
101     temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, Alpha_exp);
102     Alpha_hi = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
103     Alpha_low = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
104             - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)Alpha_hi, 16)), 1);
105 
106     // Perform the iterative calculations in the Levinson-Durbin algorithm
107 
108     for (i = 2; i <= order; i++)
109     {
110         /*                    ----
111          temp1W32 =  R[i] + > R[j]*A[i-j]
112          /
113          ----
114          j=1..i-1
115          */
116 
117         temp1W32 = 0;
118 
119         for (j = 1; j < i; j++)
120         {
121             // temp1W32 is in Q31
122             temp1W32 += ((WEBRTC_SPL_MUL_16_16(R_hi[j], A_hi[i-j]) << 1)
123                     + (((WEBRTC_SPL_MUL_16_16(R_hi[j], A_low[i-j]) >> 15)
124                             + (WEBRTC_SPL_MUL_16_16(R_low[j], A_hi[i-j]) >> 15)) << 1));
125         }
126 
127         temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, 4);
128         temp1W32 += (WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)R_hi[i], 16)
129                 + WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)R_low[i], 1));
130 
131         // K = -temp1W32 / Alpha
132         temp2W32 = WEBRTC_SPL_ABS_W32(temp1W32); // abs(temp1W32)
133         temp3W32 = WebRtcSpl_DivW32HiLow(temp2W32, Alpha_hi, Alpha_low); // abs(temp1W32)/Alpha
134 
135         // Put the sign of temp1W32 back again
136         if (temp1W32 > 0)
137         {
138             temp3W32 = -temp3W32;
139         }
140 
141         // Use the Alpha shifts from earlier to de-normalize
142         norm = WebRtcSpl_NormW32(temp3W32);
143         if ((Alpha_exp <= norm) || (temp3W32 == 0))
144         {
145             temp3W32 = WEBRTC_SPL_LSHIFT_W32(temp3W32, Alpha_exp);
146         } else
147         {
148             if (temp3W32 > 0)
149             {
150                 temp3W32 = (WebRtc_Word32)0x7fffffffL;
151             } else
152             {
153                 temp3W32 = (WebRtc_Word32)0x80000000L;
154             }
155         }
156 
157         // Put K on hi and low format
158         K_hi = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp3W32, 16);
159         K_low = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp3W32
160                 - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)K_hi, 16)), 1);
161 
162         // Store Reflection coefficient in Q15
163         K[i - 1] = K_hi;
164 
165         // Test for unstable filter.
166         // If unstable return 0 and let the user decide what to do in that case
167 
168         if ((WebRtc_Word32)WEBRTC_SPL_ABS_W16(K_hi) > (WebRtc_Word32)32750)
169         {
170             return 0; // Unstable filter
171         }
172 
173         /*
174          Compute updated LPC coefficient: Anew[i]
175          Anew[j]= A[j] + K*A[i-j]   for j=1..i-1
176          Anew[i]= K
177          */
178 
179         for (j = 1; j < i; j++)
180         {
181             // temp1W32 = A[j] in Q27
182             temp1W32 = WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_hi[j],16)
183                     + WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_low[j],1);
184 
185             // temp1W32 += K*A[i-j] in Q27
186             temp1W32 += ((WEBRTC_SPL_MUL_16_16(K_hi, A_hi[i-j])
187                     + (WEBRTC_SPL_MUL_16_16(K_hi, A_low[i-j]) >> 15)
188                     + (WEBRTC_SPL_MUL_16_16(K_low, A_hi[i-j]) >> 15)) << 1);
189 
190             // Put Anew in hi and low format
191             A_upd_hi[j] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
192             A_upd_low[j] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
193                     - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_upd_hi[j], 16)), 1);
194         }
195 
196         // temp3W32 = K in Q27 (Convert from Q31 to Q27)
197         temp3W32 = WEBRTC_SPL_RSHIFT_W32(temp3W32, 4);
198 
199         // Store Anew in hi and low format
200         A_upd_hi[i] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp3W32, 16);
201         A_upd_low[i] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp3W32
202                 - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_upd_hi[i], 16)), 1);
203 
204         // Alpha = Alpha * (1-K^2)
205 
206         temp1W32 = (((WEBRTC_SPL_MUL_16_16(K_hi, K_low) >> 14)
207                 + WEBRTC_SPL_MUL_16_16(K_hi, K_hi)) << 1); // K*K in Q31
208 
209         temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
210         temp1W32 = (WebRtc_Word32)0x7fffffffL - temp1W32; // 1 - K*K  in Q31
211 
212         // Convert 1- K^2 in hi and low format
213         tmp_hi = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
214         tmp_low = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
215                 - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)tmp_hi, 16)), 1);
216 
217         // Calculate Alpha = Alpha * (1-K^2) in Q31
218         temp1W32 = ((WEBRTC_SPL_MUL_16_16(Alpha_hi, tmp_hi)
219                 + (WEBRTC_SPL_MUL_16_16(Alpha_hi, tmp_low) >> 15)
220                 + (WEBRTC_SPL_MUL_16_16(Alpha_low, tmp_hi) >> 15)) << 1);
221 
222         // Normalize Alpha and store it on hi and low format
223 
224         norm = WebRtcSpl_NormW32(temp1W32);
225         temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, norm);
226 
227         Alpha_hi = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(temp1W32, 16);
228         Alpha_low = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32
229                 - WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)Alpha_hi, 16)), 1);
230 
231         // Update the total normalization of Alpha
232         Alpha_exp = Alpha_exp + norm;
233 
234         // Update A[]
235 
236         for (j = 1; j <= i; j++)
237         {
238             A_hi[j] = A_upd_hi[j];
239             A_low[j] = A_upd_low[j];
240         }
241     }
242 
243     /*
244      Set A[0] to 1.0 and store the A[i] i=1...order in Q12
245      (Convert from Q27 and use rounding)
246      */
247 
248     A[0] = 4096;
249 
250     for (i = 1; i <= order; i++)
251     {
252         // temp1W32 in Q27
253         temp1W32 = WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_hi[i], 16)
254                 + WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)A_low[i], 1);
255         // Round and store upper word
256         A[i] = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32((temp1W32<<1)+(WebRtc_Word32)32768, 16);
257     }
258     return 1; // Stable filters
259 }
260