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Next: SIMULATIONS Up: AUDITORY SOUND SEGREGATION MODEL Previous: Grouping block

Separation block

The separation block determines Ak(t), Bk(t), $\theta_{1k}(t)$, and $\theta_{2k}(t)$ from Sk(t) and $\phi_k(t)$ using constraints (ii) and (iv) in the determined concurrent time-frequency region. In this paper, the improvement of the auditory sound segregation model is to reconsider the constraints on the continuity of $\theta_{1k}(t)$ as well as the constraints on the continuity of Ak(t) and F0(t). Constraint (ii) is implemented such that Ck,R(t) and Dk,R(t) are linear (R=1) polynomials, in order to reduce the computational cost of estimating Ck,R(t) and Dk,R(t). In this assumption, Ak(t) and $\theta_{1k}(t)$, which can be allowed to undergo a temporal change in region, constrain the second-order polynomials ( $A_k(t)=\int C_{k,1}(t)dt+C_{k,0}'$ and $\theta_{1k}(t)=\int D_{k,1}(t)+D_{k,0}'$). Then, substituting dAk(t)/dt=Ck,R(t) into Eq. ([*]), we get the linear differential equation of the input phase difference $\theta_k(t)=\theta_{2k}(t)-\theta_{1k}(t)$. By solving this equation, a general solution is determined by

 \begin{displaymath}\theta_k(t)=\arctan\left(\frac{S_k(t)\sin(\phi_k(t)-\theta_{1k}(t))}{S_k(t)\cos(\phi_k(t)-\theta_{1k}(t))+C_k(t)}\right),
\end{displaymath} (6)

where $C_k(t)=-\int C_{k,R}(t)dt-C_{k,0}=-A_k(t)$ [7].

The signal flow of the separation block is shown in Fig. [*]. In the segment Th-Th-1 which can be determined by E0,R(t)=0, Ak(t), Bk(t), $\theta_{1k}(t)$, and $\theta_{2k}(t)$ are determined by the following steps. First, the estimated regions, $\hat{C}_{k,0}(t)-P_k(t) \leq C_{k,1}(t) \leq \hat{C}_{k,0}(t)+P_k(t)$ and $\hat{D}_{k,0}(t)-Q_k(t) \leq D_{k,1}(t) \leq \hat{D}_{k,0}(t)+Q_k(t)$, are determined by using the Kalman filter, where $\hat{C}_{k,0}(t)$ and $\hat{D}_{k,0}(t)$ are the estimated values and Pk(t) and Qk(t) are the estimated errors. Next, the candidates of Ck,1(t) at any Dk,1(t) are selected by using the spline interpolation in the estimated error region. Then, $\hat{C}_{k,1}(t)$ is determined by using

 \begin{displaymath}\hat{C}_{k,1}=\mathop{\arg\max}_{\hat{C}_{k,0}-P_k\leq C_{k,1...
...\vert\hat{A}_k\vert\vert \vert\vert\hat{\hat{A}}_k\vert\vert},
\end{displaymath} (7)

where $\hat{A}_k(t)$ is obtained by the spline interpolation and $\hat{\hat{A}}_k(t)$ is determined in across-channel that satisfies constraint (iii). Finally, $\hat{D}_{k,1}(t)$ is determined by using

 \begin{displaymath}\hat{D}_{k,1}=\mathop{\arg\max}_{\hat{D}_{k,0}-Q_k\leq D_{k,1...
...\vert\hat{A}_k\vert\vert \vert\vert\hat{\hat{A}}_k\vert\vert}.
\end{displaymath} (8)

Since $\theta_{1k}(t)$ and $\theta_k(t)$ are determined from $\hat{D}_{k,1}(t)$ and $\hat{C}_{k,1}(t)$, Ak(t), Bk(t), and $\theta_{2k}(t)$ can be determined from Eq. ([*]), Eq. ([*]), and $\theta_{2k}(t)=\theta_k(t)+\theta_{1k}(t)$, respectively.


  
Figure: Signal processing of a separation block.
\begin{figure}\center
\epsfile{file=FIGURE/u003Fig2.eps,width=0.98\linewidth}
\end{figure}


next up previous
Next: SIMULATIONS Up: AUDITORY SOUND SEGREGATION MODEL Previous: Grouping block
Masashi Unoki
2000-10-26