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 "webrtc/common_audio/signal_processing/include/signal_processing_library.h"
19
20#define SPL_LEVINSON_MAXORDER 20
21
22int16_t WebRtcSpl_LevinsonDurbin(const int32_t* R, int16_t* A, int16_t* K,
23                                 size_t order)
24{
25    size_t i, j;
26    // Auto-correlation coefficients in high precision
27    int16_t R_hi[SPL_LEVINSON_MAXORDER + 1], R_low[SPL_LEVINSON_MAXORDER + 1];
28    // LPC coefficients in high precision
29    int16_t A_hi[SPL_LEVINSON_MAXORDER + 1], A_low[SPL_LEVINSON_MAXORDER + 1];
30    // LPC coefficients for next iteration
31    int16_t A_upd_hi[SPL_LEVINSON_MAXORDER + 1], A_upd_low[SPL_LEVINSON_MAXORDER + 1];
32    // Reflection coefficient in high precision
33    int16_t K_hi, K_low;
34    // Prediction gain Alpha in high precision and with scale factor
35    int16_t Alpha_hi, Alpha_low, Alpha_exp;
36    int16_t tmp_hi, tmp_low;
37    int32_t temp1W32, temp2W32, temp3W32;
38    int16_t norm;
39
40    // Normalize the autocorrelation R[0]...R[order+1]
41
42    norm = WebRtcSpl_NormW32(R[0]);
43
44    for (i = 0; i <= order; ++i)
45    {
46        temp1W32 = WEBRTC_SPL_LSHIFT_W32(R[i], norm);
47        // Put R in hi and low format
48        R_hi[i] = (int16_t)(temp1W32 >> 16);
49        R_low[i] = (int16_t)((temp1W32 - ((int32_t)R_hi[i] << 16)) >> 1);
50    }
51
52    // K = A[1] = -R[1] / R[0]
53
54    temp2W32 = WEBRTC_SPL_LSHIFT_W32((int32_t)R_hi[1],16)
55            + WEBRTC_SPL_LSHIFT_W32((int32_t)R_low[1],1); // R[1] in Q31
56    temp3W32 = WEBRTC_SPL_ABS_W32(temp2W32); // abs R[1]
57    temp1W32 = WebRtcSpl_DivW32HiLow(temp3W32, R_hi[0], R_low[0]); // abs(R[1])/R[0] in Q31
58    // Put back the sign on R[1]
59    if (temp2W32 > 0)
60    {
61        temp1W32 = -temp1W32;
62    }
63
64    // Put K in hi and low format
65    K_hi = (int16_t)(temp1W32 >> 16);
66    K_low = (int16_t)((temp1W32 - ((int32_t)K_hi << 16)) >> 1);
67
68    // Store first reflection coefficient
69    K[0] = K_hi;
70
71    temp1W32 >>= 4;  // A[1] in Q27.
72
73    // Put A[1] in hi and low format
74    A_hi[1] = (int16_t)(temp1W32 >> 16);
75    A_low[1] = (int16_t)((temp1W32 - ((int32_t)A_hi[1] << 16)) >> 1);
76
77    // Alpha = R[0] * (1-K^2)
78
79    temp1W32 = ((K_hi * K_low >> 14) + K_hi * K_hi) << 1;  // = k^2 in Q31
80
81    temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
82    temp1W32 = (int32_t)0x7fffffffL - temp1W32; // temp1W32 = (1 - K[0]*K[0]) in Q31
83
84    // Store temp1W32 = 1 - K[0]*K[0] on hi and low format
85    tmp_hi = (int16_t)(temp1W32 >> 16);
86    tmp_low = (int16_t)((temp1W32 - ((int32_t)tmp_hi << 16)) >> 1);
87
88    // Calculate Alpha in Q31
89    temp1W32 = (R_hi[0] * tmp_hi + (R_hi[0] * tmp_low >> 15) +
90        (R_low[0] * tmp_hi >> 15)) << 1;
91
92    // Normalize Alpha and put it in hi and low format
93
94    Alpha_exp = WebRtcSpl_NormW32(temp1W32);
95    temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, Alpha_exp);
96    Alpha_hi = (int16_t)(temp1W32 >> 16);
97    Alpha_low = (int16_t)((temp1W32 - ((int32_t)Alpha_hi << 16)) >> 1);
98
99    // Perform the iterative calculations in the Levinson-Durbin algorithm
100
101    for (i = 2; i <= order; i++)
102    {
103        /*                    ----
104         temp1W32 =  R[i] + > R[j]*A[i-j]
105         /
106         ----
107         j=1..i-1
108         */
109
110        temp1W32 = 0;
111
112        for (j = 1; j < i; j++)
113        {
114          // temp1W32 is in Q31
115          temp1W32 += (R_hi[j] * A_hi[i - j] << 1) +
116              (((R_hi[j] * A_low[i - j] >> 15) +
117              (R_low[j] * A_hi[i - j] >> 15)) << 1);
118        }
119
120        temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, 4);
121        temp1W32 += (WEBRTC_SPL_LSHIFT_W32((int32_t)R_hi[i], 16)
122                + WEBRTC_SPL_LSHIFT_W32((int32_t)R_low[i], 1));
123
124        // K = -temp1W32 / Alpha
125        temp2W32 = WEBRTC_SPL_ABS_W32(temp1W32); // abs(temp1W32)
126        temp3W32 = WebRtcSpl_DivW32HiLow(temp2W32, Alpha_hi, Alpha_low); // abs(temp1W32)/Alpha
127
128        // Put the sign of temp1W32 back again
129        if (temp1W32 > 0)
130        {
131            temp3W32 = -temp3W32;
132        }
133
134        // Use the Alpha shifts from earlier to de-normalize
135        norm = WebRtcSpl_NormW32(temp3W32);
136        if ((Alpha_exp <= norm) || (temp3W32 == 0))
137        {
138            temp3W32 = WEBRTC_SPL_LSHIFT_W32(temp3W32, Alpha_exp);
139        } else
140        {
141            if (temp3W32 > 0)
142            {
143                temp3W32 = (int32_t)0x7fffffffL;
144            } else
145            {
146                temp3W32 = (int32_t)0x80000000L;
147            }
148        }
149
150        // Put K on hi and low format
151        K_hi = (int16_t)(temp3W32 >> 16);
152        K_low = (int16_t)((temp3W32 - ((int32_t)K_hi << 16)) >> 1);
153
154        // Store Reflection coefficient in Q15
155        K[i - 1] = K_hi;
156
157        // Test for unstable filter.
158        // If unstable return 0 and let the user decide what to do in that case
159
160        if ((int32_t)WEBRTC_SPL_ABS_W16(K_hi) > (int32_t)32750)
161        {
162            return 0; // Unstable filter
163        }
164
165        /*
166         Compute updated LPC coefficient: Anew[i]
167         Anew[j]= A[j] + K*A[i-j]   for j=1..i-1
168         Anew[i]= K
169         */
170
171        for (j = 1; j < i; j++)
172        {
173            // temp1W32 = A[j] in Q27
174            temp1W32 = WEBRTC_SPL_LSHIFT_W32((int32_t)A_hi[j],16)
175                    + WEBRTC_SPL_LSHIFT_W32((int32_t)A_low[j],1);
176
177            // temp1W32 += K*A[i-j] in Q27
178            temp1W32 += (K_hi * A_hi[i - j] + (K_hi * A_low[i - j] >> 15) +
179                (K_low * A_hi[i - j] >> 15)) << 1;
180
181            // Put Anew in hi and low format
182            A_upd_hi[j] = (int16_t)(temp1W32 >> 16);
183            A_upd_low[j] = (int16_t)(
184                (temp1W32 - ((int32_t)A_upd_hi[j] << 16)) >> 1);
185        }
186
187        // temp3W32 = K in Q27 (Convert from Q31 to Q27)
188        temp3W32 >>= 4;
189
190        // Store Anew in hi and low format
191        A_upd_hi[i] = (int16_t)(temp3W32 >> 16);
192        A_upd_low[i] = (int16_t)(
193            (temp3W32 - ((int32_t)A_upd_hi[i] << 16)) >> 1);
194
195        // Alpha = Alpha * (1-K^2)
196
197        temp1W32 = ((K_hi * K_low >> 14) + K_hi * K_hi) << 1;  // K*K in Q31
198
199        temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
200        temp1W32 = (int32_t)0x7fffffffL - temp1W32; // 1 - K*K  in Q31
201
202        // Convert 1- K^2 in hi and low format
203        tmp_hi = (int16_t)(temp1W32 >> 16);
204        tmp_low = (int16_t)((temp1W32 - ((int32_t)tmp_hi << 16)) >> 1);
205
206        // Calculate Alpha = Alpha * (1-K^2) in Q31
207        temp1W32 = (Alpha_hi * tmp_hi + (Alpha_hi * tmp_low >> 15) +
208            (Alpha_low * tmp_hi >> 15)) << 1;
209
210        // Normalize Alpha and store it on hi and low format
211
212        norm = WebRtcSpl_NormW32(temp1W32);
213        temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, norm);
214
215        Alpha_hi = (int16_t)(temp1W32 >> 16);
216        Alpha_low = (int16_t)((temp1W32 - ((int32_t)Alpha_hi << 16)) >> 1);
217
218        // Update the total normalization of Alpha
219        Alpha_exp = Alpha_exp + norm;
220
221        // Update A[]
222
223        for (j = 1; j <= i; j++)
224        {
225            A_hi[j] = A_upd_hi[j];
226            A_low[j] = A_upd_low[j];
227        }
228    }
229
230    /*
231     Set A[0] to 1.0 and store the A[i] i=1...order in Q12
232     (Convert from Q27 and use rounding)
233     */
234
235    A[0] = 4096;
236
237    for (i = 1; i <= order; i++)
238    {
239        // temp1W32 in Q27
240        temp1W32 = WEBRTC_SPL_LSHIFT_W32((int32_t)A_hi[i], 16)
241                + WEBRTC_SPL_LSHIFT_W32((int32_t)A_low[i], 1);
242        // Round and store upper word
243        A[i] = (int16_t)(((temp1W32 << 1) + 32768) >> 16);
244    }
245    return 1; // Stable filters
246}
247