## 3 Proposed Method
### High-Quefrency Boosting via Sub-Band Cepstrum Conversion and Fusion  
The sub-band cepstrum conversion and weighted fusion is designed to improve the noise robustness of the whole conversion system. Figure 2 shows the sub-band fusion BLSTM network for MCEPs. BLSTM can be created by stacking multiple hidden layers. In the proposed model, two BLSTMs (i.e., BLSTM1 and BLSTM2 in Figure 2) were used, and both of them were composed of three hidden layers.  
The motivation for designing a sub-band cepstrum conversion system was that when voice is contaminated by strong noises, the high quefrency components of cepstrum failed to be recovered accurately, given our previous experiences. Simply training a conversion network may not be sufficient to recover the full-band cepstrum accurately, which could be overcome by a converging cepstrum in the sub-bands. In the proposed model, BLSTM1 was used for training and converting a full-band cepstrum, because full-band MCEPs are a high-dimensional cepstrum, which contains a large amount of data, such that the training data is sufficient and is of benefit to training appropriate network parameters and making the network convergent. An additional BLSTM, BLSTM2, was designed to convert and generate the high-quefrency part of the MCEPs by mapping the full-band information of the source MCEPs with the high-quefrency band of the target MCEPs. Finally, the two networks were fused. By applying the fusion coefficients extracted in the training phase to the conversion phase, the sub-band cepstral parameters were smoothly connected, and then the discontinuity in the process of cepstrum splicing was alleviated.  
Figure 1: Voice conversion flow chart of sub-band cepstrum weighted fusion bidirectional long short-term memory (BLSTM). DTW: dynamic time warping.  
As shown in Figure 3, the trained BLSTM1 and BLSTM2 were used to convert \(MC_{full}\) to \(MC_{full}\)\({}^{\#}\) and \(MC_{full}\) to \(mcep_{high2}\), respectively. The \(mcep_{high1}\) and \(mcep_{low1}\) were from \(MC_{full}\)\({}^{\#}\) and the \(mcep_{high2}\) was converted from \(MC_{full}\) by BLSTM2. \(\alpha\) was the weight parameter used to perform sub-band cepstrum fusion.  
In a sub-band cepstrum conversion, the full-band cepstrum is divided into two parts with equal numbers of cepstral coefficients: one represents the low-quefrency sub-band and the other represents the high-quefrency sub-band. The two sub-bands are subsequently treated in different ways. When the converted sub-band cepstrum is ready, the two parts are fused by a weight parameter alpha (i.e., \(\alpha\) in Figure 3). The specific algorithm in the fusion process is given as:  
Figure 3: The diagram of the cepstrum-weighted fusion process, where the MC represents the full band MCEPs in different cases.  
Figure 2: The flowchart of voice conversion with sub-band cepstrum conversion by BLSTMs. MCEPs: Mel-cepstral coefficients  
\[\begin{split}& MC_{\text{\emph{high fusion}}}=\alpha\times mcep_{\text{ \emph{high1}}}+(1-\alpha)\times mcep_{\text{\emph{high2}}}\\ & MC_{\text{\emph{low1}}}=mcep_{\text{\emph{low1}}}\\ & MC_{\text{\emph{full fusion}}}=[MC_{\text{\emph{low1}}};MC_{\text{ \emph{high fusion}}}]\end{split}. \tag{9}\]