轉載自：https://www.cnblogs.com/damizhou/p/11318668.html
摘要：
在上一篇的文檔中，分析unimrcp中vad算法的諸多弊端，但是有沒有一種更好的算法來取代呢。目前有兩種方式 1. GMM 2. DNN。
其中鼎鼎大名的WebRTC VAD就是採用了GMM 算法來完成voice active dector。今天筆者重點介紹WebRTC VAD算法。在後面的文章中，
我們在刨析DNN在VAD的中應用。下面的章節中，將介紹WebRTC的檢測原理。
原理：
首先呢，我們要了解一下人聲和樂器的頻譜範圍，下圖是音頻的頻譜。
根據音頻的頻譜劃分了6個子帶，80Hz~250Hz，250Hz~500Hz,500Hz~1K,1K~2K,2K~3K,3K~4K，分別計算出每個子帶的特徵。
步驟：
1. 準備工作
1.1 WebRTC的檢測模式分為了4種:
0: Normal, 1. low Bitrate 2.Aggressive 3. Very Aggressive ，其激進程序與數值大小相關，可以根據實際的使用在初始化的時候可以配置。
set mode code
1.2 vad 支持三種幀長，80/10ms 160/20ms 240/30ms
採樣這三種幀長，是由語音信號的特點決定的，語音信號是短時平穩信號，在10ms-30ms之間被看成平穩信號，高斯馬爾可夫等比較信號處理方法基於的前提是信號是平穩的。
1.3 支持頻率： 8khz 16khz 32khz 48khz
WebRTC 支持8kHz 16kHz 32kHz 48kHz的音頻，但是WebRTC首先都將16kHz 32kHz 48kHz首先降頻到8kHz，再進行處理。
1 int16_t speech_nb[240]; // 30 ms in 8 kHz.
2 const size_t kFrameLen10ms = (size_t) (fs / 100);
3 const size_t kFrameLen10ms8khz = 80;
4 size_t num_10ms_frames = frame_length / kFrameLen10ms;
5 int i = 0;
6 for (i = 0; i < num_10ms_frames; i++) {
7 resampleData(audio_frame, fs, kFrameLen10ms, &speech_nb[i * kFrameLen10ms8khz],
8 8000);
9 }
10 size_t new_frame_length = frame_length * 8000 / fs;
11 // Do VAD on an 8 kHz signal
12 vad = WebRtcVad_CalcVad8khz(self, speech_nb, new_frame_length);
2. 通過高斯模型計算子帶能量，並且計算靜音和語音的概率。
WebRtcVad_CalcVad8khz 函數計算特徵量，其特徵包括了6個子帶的能量。計算後的特徵存在feature_vector中。
View Code
WebRtcVad_GaussianProbability計算噪音和語音的分佈概率，對於每一個特徵，求其似然比，計算加權對數似然比。如果6個特徵中其中有一個超過了閾值，就認為是語音。
View Code
3. 最後更新模型方差
3.1 通過WebRtcVad_FindMinimum 求出最小值更新方差，計算噪聲加權平均值。
3.2 更新模型參數，噪音模型均值更新、語音模型均值更新、噪聲模型方差更新、語音模型方差更新。
1 // Update the model parameters.
2 maxspe = 12800;
3 for (channel = 0; channel < kNumChannels; channel++) {
4
5 // Get minimum value in past which is used for long term correction in Q4.
6 feature_minimum = WebRtcVad_FindMinimum(self, features[channel], channel);
7
8 // Compute the "global" mean, that is the sum of the two means weighted.
9 noise_global_mean = WeightedAverage(&self->noise_means[channel], 0,
10 &kNoiseDataWeights[channel]);
11 tmp1_s16 = (int16_t) (noise_global_mean >> 6); // Q8
12
13 for (k = 0; k < kNumGaussians; k++) {
14 gaussian = channel + k * kNumChannels;
15
16 nmk = self->noise_means[gaussian];
17 smk = self->speech_means[gaussian];
18 nsk = self->noise_stds[gaussian];
19 ssk = self->speech_stds[gaussian];
20
21 // Update noise mean vector if the frame consists of noise only.
22 nmk2 = nmk;
23 if (!vadflag) {
24 // deltaN = (x-mu)/sigma^2
25 // ngprvec[k] = |noise_probability[k]| /
26 // (|noise_probability[0]| + |noise_probability[1]|)
27
28 // (Q14 * Q11 >> 11) = Q14.
29 delt = (int16_t) ((ngprvec[gaussian] * deltaN[gaussian]) >> 11);
30 // Q7 + (Q14 * Q15 >> 22) = Q7.
31 nmk2 = nmk + (int16_t) ((delt * kNoiseUpdateConst) >> 22);
32 }
33
34 // Long term correction of the noise mean.
35 // Q8 - Q8 = Q8.
36 ndelt = (feature_minimum << 4) - tmp1_s16;
37 // Q7 + (Q8 * Q8) >> 9 = Q7.
38 nmk3 = nmk2 + (int16_t) ((ndelt * kBackEta) >> 9);
39
40 // Control that the noise mean does not drift to much.
41 tmp_s16 = (int16_t) ((k + 5) << 7);
42 if (nmk3 < tmp_s16) {
43 nmk3 = tmp_s16;
44 }
45 tmp_s16 = (int16_t) ((72 + k - channel) << 7);
46 if (nmk3 > tmp_s16) {
47 nmk3 = tmp_s16;
48 }
49 self->noise_means[gaussian] = nmk3;
50
51 if (vadflag) {
52 // Update speech mean vector:
53 // |deltaS| = (x-mu)/sigma^2
54 // sgprvec[k] = |speech_probability[k]| /
55 // (|speech_probability[0]| + |speech_probability[1]|)
56
57 // (Q14 * Q11) >> 11 = Q14.
58 delt = (int16_t) ((sgprvec[gaussian] * deltaS[gaussian]) >> 11);
59 // Q14 * Q15 >> 21 = Q8.
60 tmp_s16 = (int16_t) ((delt * kSpeechUpdateConst) >> 21);
61 // Q7 + (Q8 >> 1) = Q7. With rounding.
62 smk2 = smk + ((tmp_s16 + 1) >> 1);
63
64 // Control that the speech mean does not drift to much.
65 maxmu = maxspe + 640;
66 if (smk2 < kMinimumMean[k]) {
67 smk2 = kMinimumMean[k];
68 }
69 if (smk2 > maxmu) {
70 smk2 = maxmu;
71 }
72 self->speech_means[gaussian] = smk2; // Q7.
73
74 // (Q7 >> 3) = Q4. With rounding.
75 tmp_s16 = ((smk + 4) >> 3);
76
77 tmp_s16 = features[channel] - tmp_s16; // Q4
78 // (Q11 * Q4 >> 3) = Q12.
79 tmp1_s32 = (deltaS[gaussian] * tmp_s16) >> 3;
80 tmp2_s32 = tmp1_s32 - 4096;
81 tmp_s16 = sgprvec[gaussian] >> 2;
82 // (Q14 >> 2) * Q12 = Q24.
83 tmp1_s32 = tmp_s16 * tmp2_s32;
84
85 tmp2_s32 = tmp1_s32 >> 4; // Q20
86
87 // 0.1 * Q20 / Q7 = Q13.
88 if (tmp2_s32 > 0) {
89 tmp_s16 = (int16_t) DivW32W16(tmp2_s32, ssk * 10);
90 } else {
91 tmp_s16 = (int16_t) DivW32W16(-tmp2_s32, ssk * 10);
92 tmp_s16 = -tmp_s16;
93 }
94 // Divide by 4 giving an update factor of 0.025 (= 0.1 / 4).
95 // Note that division by 4 equals shift by 2, hence,
96 // (Q13 >> 8) = (Q13 >> 6) / 4 = Q7.
97 tmp_s16 += 128; // Rounding.
98 ssk += (tmp_s16 >> 8);
99 if (ssk < kMinStd) {
100 ssk = kMinStd;
101 }
102 self->speech_stds[gaussian] = ssk;
103 } else {
104 // Update GMM variance vectors.
105 // deltaN * (features[channel] - nmk) - 1
106 // Q4 - (Q7 >> 3) = Q4.
107 tmp_s16 = features[channel] - (nmk >> 3);
108 // (Q11 * Q4 >> 3) = Q12.
109 tmp1_s32 = (deltaN[gaussian] * tmp_s16) >> 3;
110 tmp1_s32 -= 4096;
111
112 // (Q14 >> 2) * Q12 = Q24.
113 tmp_s16 = (ngprvec[gaussian] + 2) >> 2;
114 tmp2_s32 = (tmp_s16 * tmp1_s32);
115 // tmp2_s32 = OverflowingMulS16ByS32ToS32(tmp_s16, tmp1_s32);
116 // Q20 * approx 0.001 (2^-10=0.0009766), hence,
117 // (Q24 >> 14) = (Q24 >> 4) / 2^10 = Q20.
118 tmp1_s32 = tmp2_s32 >> 14;
119
120 // Q20 / Q7 = Q13.
121 if (tmp1_s32 > 0) {
122 tmp_s16 = (int16_t) DivW32W16(tmp1_s32, nsk);
123 } else {
124 tmp_s16 = (int16_t) DivW32W16(-tmp1_s32, nsk);
125 tmp_s16 = -tmp_s16;
126 }
127 tmp_s16 += 32; // Rounding
128 nsk += tmp_s16 >> 6; // Q13 >> 6 = Q7.
129 if (nsk < kMinStd) {
130 nsk = kMinStd;
131 }
132 self->noise_stds[gaussian] = nsk;
133 }
134 }
135
136 // Separate models if they are too close.
137 // |noise_global_mean| in Q14 (= Q7 * Q7).
138 noise_global_mean = WeightedAverage(&self->noise_means[channel], 0,
139 &kNoiseDataWeights[channel]);
140
141 // |speech_global_mean| in Q14 (= Q7 * Q7).
142 speech_global_mean = WeightedAverage(&self->speech_means[channel], 0,
143 &kSpeechDataWeights[channel]);
144
145 // |diff| = "global" speech mean - "global" noise mean.
146 // (Q14 >> 9) - (Q14 >> 9) = Q5.
147 diff = (int16_t) (speech_global_mean >> 9) -
148 (int16_t) (noise_global_mean >> 9);
149 if (diff < kMinimumDifference[channel]) {
150 tmp_s16 = kMinimumDifference[channel] - diff;
151
152 // |tmp1_s16| = ~0.8 * (kMinimumDifference - diff) in Q7.
153 // |tmp2_s16| = ~0.2 * (kMinimumDifference - diff) in Q7.
154 tmp1_s16 = (int16_t) ((13 * tmp_s16) >> 2);
155 tmp2_s16 = (int16_t) ((3 * tmp_s16) >> 2);
156
157 // Move Gaussian means for speech model by |tmp1_s16| and update
158 // |speech_global_mean|. Note that |self->speech_means[channel]| is
159 // changed after the call.
160 speech_global_mean = WeightedAverage(&self->speech_means[channel],
161 tmp1_s16,
162 &kSpeechDataWeights[channel]);
163
164 // Move Gaussian means for noise model by -|tmp2_s16| and update
165 noise_global_mean = WeightedAverage(&self->noise_means[channel],
166 -tmp2_s16,
167 &kNoiseDataWeights[channel]);
168 }
169
170 // Control that the speech & noise means do not drift to much.
171 maxspe = kMaximumSpeech[channel];
172 tmp2_s16 = (int16_t) (speech_global_mean >> 7);
173 if (tmp2_s16 > maxspe) {
174 // Upper limit of speech model.
175 tmp2_s16 -= maxspe;
176
177 for (k = 0; k < kNumGaussians; k++) {
178 self->speech_means[channel + k * kNumChannels] -= tmp2_s16;
179 }
180 }
181
182 tmp2_s16 = (int16_t) (noise_global_mean >> 7);
183 if (tmp2_s16 > kMaximumNoise[channel]) {
184 tmp2_s16 -= kMaximumNoise[channel];
185
186 for (k = 0; k < kNumGaussians; k++) {
187 self->noise_means[channel + k * kNumChannels] -= tmp2_s16;
188 }
189 }
190 }
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