@[TOC](A Dual-Microphone Algorithm That Can Cope With Competing-Talkers Scenarios) 1
这里介绍一种基于相干函数的双麦降噪算法，上一篇 2 S N R E s t i m a t i o n SNR Estimation S N R E s t i m a t i o n
信号定义以及相干函数的计算都是跟上一篇 相同，这里就不重复，直接跳到相干函数跟信噪比的公式：(1) Γ ^ y 1 y 2 ( ω ) = [ c o s ( ω τ ) + j s i n ( ω τ ) ] S N R ^ 1 + S N R ^ + [ c o s ( ω τ c o s θ ) + j s i n ( ω τ c o s θ ) ] 1 1 + S N R ^
\hat{\Gamma }_{y_{1}y_{2}}(\omega)=[cos(\omega \tau)+jsin(\omega \tau)]\frac{\hat{SNR}}{1+\hat{SNR}}+[cos(\omega \tau cos\theta)+jsin(\omega \tau cos\theta)]\frac{1}{1+\hat{SNR}} \tag{1}
Γ ^ y 1 y 2 ( ω ) = [ c o s ( ω τ ) + j s i n ( ω τ ) ] 1 + S N R ^ S N R ^ + [ c o s ( ω τ c o s θ ) + j s i n ( ω τ c o s θ ) ] 1 + S N R ^ 1 ( 1 ) Γ ^ y 1 y 2 ( ω ) \hat{\Gamma }_{y_{1}y_{2}}(\omega) Γ ^ y 1 y 2 ( ω ) (2) ℜ = S N ^ R 1 + S N ^ R cos ω ˙ + 1 1 + S N ^ R cos α
\Re=\frac{\mathrm{S} \hat{\mathrm{N}} \mathrm{R}}{1+\mathrm{S} \hat{\mathrm{N}} \mathrm{R}} \cos \dot{\omega}+\frac{1}{1+\mathrm{S} \hat{\mathrm{N}} \mathrm{R}} \cos \alpha\tag{2}
ℜ = 1 + S N ^ R S N ^ R cos ω ˙ + 1 + S N ^ R 1 cos α ( 2 ) (3) ℑ = S N R ^ 1 + S N ^ R sin ω ˙ + 1 1 + S N R ^ sin α
\Im=\frac{\hat{SNR}}{1+\mathrm{S} \hat{\mathrm{N}} \mathrm{R}} \sin \dot{\omega}+\frac{1}{1+\hat{SNR}} \sin \alpha \tag{3}
ℑ = 1 + S N ^ R S N R ^ sin ω ˙ + 1 + S N R ^ 1 sin α ( 3 ) ω ˙ = ω τ ， α = ω ˙ c o s θ \dot{\omega}=\omega \tau，\alpha=\dot{\omega} cos\theta ω ˙ = ω τ ， α = ω ˙ c o s θ S N R ^ 和 α \hat{SNR}和\alpha S N R ^ 和 α S N R ^ 和 α \hat{SNR}和\alpha S N R ^ 和 α S N R ^ \hat{SNR} S N R ^ α \alpha α S N ^ R \mathrm{S} \hat{\mathrm{N}} \mathrm{R} S N ^ R α \alpha α (4) S N ^ R = sin α − ℑ ℑ − sin ω ˙
\mathrm{S} \hat{\mathrm{N}} \mathrm{R}=\frac{\sin \alpha-\Im}{\Im-\sin \dot{\omega}} \tag{4}
S N ^ R = ℑ − sin ω ˙ sin α − ℑ ( 4 ) (5) { A = ℑ − sin ω ˙ B = cos ω ˙ − ℜ C = ℜ sin ω ˙ − ℑ cos ω ˙
\left\{\begin{array}{l}{A=\Im-\sin \dot{\omega}} \\ {B=\cos \dot{\omega}-\Re} \\ {C=\Re \sin \dot{\omega}-\Im \cos \dot{\omega}}\end{array}\right. \tag{5}
⎩ ⎨ ⎧ A = ℑ − sin ω ˙ B = cos ω ˙ − ℜ C = ℜ sin ω ˙ − ℑ cos ω ˙ ( 5 ) (6) T = 1 − ℜ cos ω ˙ − ℑ sin ω ˙
T=1-\Re \cos \dot{\omega}-\Im \sin \dot{\omega} \tag{6}
T = 1 − ℜ cos ω ˙ − ℑ sin ω ˙ ( 6 ) (7) sin α = − B ∗ C + A ∗ T A 2 + B 2
\sin \alpha=\frac{-B*C+A*T}{A^2+B^2} \tag{7}
sin α = A 2 + B 2 − B ∗ C + A ∗ T ( 7 ) S N ^ R \mathrm{S} \hat{\mathrm{N}} \mathrm{R} S N ^ R (８) G ( ω , k ) = SNR ( ω , k ) SNR ( ω , k ) + 1
G(\omega, k)=\sqrt{\frac{\operatorname{SNR}(\omega, k)}{\operatorname{SNR}(\omega, k)+1}} \tag{８}
G ( ω , k ) = S N R ( ω , k ) + 1 S N R ( ω , k ) ( ８ )
还是上篇一样的音频，对比下处理前后结果
Yousefian, N., & Loizou, P. C. (2013). A Dual-Microphone Algorithm That Can Cope With Competing-Talker Scenarios. IEEE Transactions on Audio, Speech, and Language Processing, 21(1), 145–155 ↩︎
Yousefian, N., & Loizou, P. (2011). A Dual-Microphone Speech Enhancement Algorithm Based on the Coherence Function. IEEE Transactions on Audio, Speech, and Language Processing. ↩︎
