Segregation algorithm

The theorem for segregation is obtained from previous lemma as follows.

Theorem 1 (Segregation algorithm)  

For the problem of segregating two acoustic sources where $\theta_{1k}(t)=0$ and $\theta_k(t)=\theta_{2k}(t)$, the input phase $\theta_k(t)$ can be determined using physical constraints 1-3 from Eqs. () and (). Therefore, this problem can be solved using the amplitude envelope S_k(t) and the output phase $\phi_k(t)$ from Eqs. ()-().

Proof. Refer to Lemma 1 and 2. $\Box$

Segregation algorithm based on Theorem 1 is shown in Fig. . When the problem of segregating two acoustic sources is to be solved using Theorem 1, signal duration which two signals exist in the same time region must be known. In Section 2, we assumed that when localized f₁(t) is added to f₂(t), the signal duration can be detected using onset and offset of f₁(t). By focusing on the temporal deviation of S_k(t) and $\phi_k(t)$, onset and offset of f₁(t) can be determined as follows:

1.

Onset $T_{\rm {on}}$ is determined by the nearest maximum point of $\vert d\phi_k(t)/dt\vert$ (within 25 ms) to the maximum point of |dS_k(t)/dt|.

2.

Offset $T_{\rm {on}}$ is determined by the nearest maximum point of $\vert d\phi_k(t)/dt\vert$ (within 25 ms) to the minimum point of |dS_k(t)/dt|.

Therefore, the segregated duration is $t_{\rm {on}} \leq t \leq t_{\rm {off}}$.