## 2 Proposed NELE Method
### Optimization Unit
Although in every optimization cycle many weights related to the current and future frames are computed, only a weight obtained for the current frame will be fixed and other weights will be updated on the next optimization cycle. After determination of a weight in each optimization, its value in all CFs is replaced. The routine for the determination of weights and updating the CFs is explained in Algorithm 1. In the Onset Enhancement (OE) method [16], a time-varying weight of a frame is determined according to the power spectrums of that frame and that of the previous frames, which are of influence because of the reverberation tail that has overlap with the current frame. In the proposed approach, in order to determine the weight of current frame, a cost function is optimized based on the power spectrum of current frame and that of the future frames. Considering the future frames in the cost function optimization implies that the effect of the filtering of the current frame on future frames will also be considered; this is not the case in the OE method. Note that the weights of the previous frames were fixed before, but their effect is still considered in Equation (12). ```
Step 1:\(k=1\) Step 2: The weight of frame number \(k\) is determined. All the upcoming CFs that are influ-enced by \(\alpha_{k,f}\) construct the \(SCK_{k}(f)\) according to Equation (12). For construction of \(SCK_{k}(f)\), previous determined weights in CFs are used and the new weight \(\alpha_{k,f}\) is determined: \(SCF_{k}(f)=fun\ (\alpha_{1,f},\alpha_{2,f},\ldots,\alpha_{k-1,f},\alpha_{k,f}, \alpha_{k+1,f},\ldots,\alpha_{p+k-1,f})\) \(\approx fun\ (\alpha_{k-P+1,f},\ldots,\alpha_{k-1,f},\alpha_{k,f},\alpha_{k+1,f}, \ldots,\alpha_{p+k-1,f})\) \(\underline{\textbf{optimization}}\) \(\underline{\textbf{optimization}}\) \(\underline{\textbf{\alpha}_{k,f}},\ldots,\alpha_{k+1,f},\ldots,\alpha_{p+k-1,f}\) For example, the \(SCK_{1}(f)\) is a function of \(\alpha_{1,f}\), \(\alpha_{2,f}\),..., \(\alpha_{p,f}\). All of these weights are determined in the first optimization. However, only \(\alpha_{1,f}\) is accepted as the final value: \(SCF_{1}=fun(\alpha_{1,f},\alpha_{2,f},\ldots,\alpha_{p,f})\) \(\underline{\textbf{optimization}}\) \(\underline{\textbf{\alpha}_{1,f}},\underline{\textbf{\alpha}_{2,f}},\ldots, \underline{\textbf{\alpha}_{p,f}}\) Step 3: All CFs that are influenced by \(\alpha_{k,f}\) are replaced by their numerical value. \(CF_{k}(f)=fun\ (\alpha_{k+p-1,f},\ldots,\alpha_{k-1,f},\alpha_{k,f})\) \(CF_{k+1}(f)=fun\ (\alpha_{k+p,f},\ldots,\alpha_{k,f},\alpha_{k+1,f})\) \(\vdots\) \(\mathrm{CF}_{k+p-1}(f)=fun\ (\alpha_{k,f},\alpha_{k+1,f},\ldots,\alpha_{k+P-1,f})\)  For example, for \(\alpha_{1,f}\): \(CF_{1}(f)=fun\ (\alpha_{1,f})\) \(CF_{2}(f)=fun\ (\underline{\textbf{\alpha}_{1,f}},\alpha_{2,f})\) \(\vdots\) \(CF_{p}(f)=fun\ (\underline{\textbf{\alpha}_{1,f}},\underline{\textbf{\alpha}_{2,f}}, \ldots,\alpha_{p,f})\) Step 4:\(k=k+1\)  If \(k<N\): go to Step 2  else finish
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**Algorithm 1** Example text of a theorem. Determination of weights \(\alpha_{1,f}\), \(\alpha_{2,f}\),..., \(\alpha_{k,f}\),..., \(\alpha_{N,f}\) in a one-third octave (\(f\)).