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 Akagi1999a]. $\hat{f}_1(t)$ 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. Onset $T_{k,\rm {on}}$ and offset $T_{k,\rm {off}}$ in X_k(t) are determined by using the nearest maximum or minimum point of $\vert{d\phi_k(t)}/{dt}\vert$ and 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 using (iii) in Table 1. $\lceil\cdot\rceil$ 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.

  

Figure: Concept of constraints related to Bregman's regularities.