Grouping block

The grouping block determines the concurrent time-frequency region of the desired signal using constraints (i) and (iii) in Table 1, and then reconstructs the segregated instantaneous amplitude and phase using the inverse wavelet transform [Unoki and Akagi1999]. $\hat{f}_1(t)$ and $\hat{f}_2(t)$ are the reconstructed f₁(t) and f₂(t).

Constraint (i) is implemented by comparing the onset/offset ( $T_{k,\rm{on}},T_{k,\rm{off}}$) of X_k(t) with the onset/offset ( $T_{\rm{S}},T_{\rm{E}}$) of $X_{\hat{\ell}}(t)$ corresponding to F₀(t), where $\Delta T_{\rm{S}}=25$ ms and $\Delta T_{\rm{E}}=50$ ms [Unoki and Akagi1999]. In this paper, onset $T_{k,\rm{on}}$ and offset $T_{k,\rm{off}}$ in X_k(t) are determined as follows.

1.

Onset $T_{k,\rm{on}}$ 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 $T_{k,\rm{off}}$ 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.

Constraint (iii) is implemented by determining the channel number corresponding to the integer multiples of F₀(t). The channel number $\ell$ of $X_\ell(t)$, in which the harmonic components exist in the output of the $\ell$-th channel, is determined by

$$\ell=\frac{K}{2}-\left\lceil \frac{\log(n\cdot F_0(t)/f_0)}{\log\alpha} \right\rceil,\quad n=1,2,\cdots, N_{F_0},$$ (13)

where $\alpha$ is the scale parameter and $\lceil\cdot\rceil$ is the ceil symbol, meaning the approximation of the closest integer value toward positive infinity. In addition, K is an even number and f₀ is the center frequency of the analyzing wavelet in the constant Q gammatone filterbank (f₀=600) [Unoki and Akagi1999].