## 3 Experiments
### Experimental Setups  
In this work, the two parallel corpora have been separated into 100 pairs of utterances for training, 20 pairs of utterances for validation, and 22 pairs of utterances for testing. We used the cepstrum analysis to obtain the Fourier cepstra of each utterance. First, a normalized Hamming window \(H(n)\) of length 512 is used to obtain the short-term temporal signals, from which the cepstral coefficients are extracted. Then, to obtain the logarithmic Fourier magnitude spectrum, a fast Fourier transformation (FFT) is applied to the 512 windowed temporal signals, followed by the calculation of the logarithm of the modulus of the complex spectrum obtained by FFT. The inverse fast Fourier transform of the logarithmic magnitude spectrum makes it possible to extract the real logarithmic cepstrum. As already detailed in Section 2.2, for each frame, the first 33 coefficients represent the cepstral vector related to the vocal tract; the next 224 define the cepstral vector related to the excitation signal, and the phase spectrum was determined by the 257 phase coefficients. Our model is an LSTM encoder-decoder based on an attention mechanism. The encoder consists of 2 BiLSTM layers as follows: a forward LSTM, which receives the input sequence in order (from \(x_{1}\) to \(x_{N}\)), and a backward LSTM, which receives the same sequence in reverse order (from \(x_{N}\) to \(x_{1}\)). Each layer contains 128 hidden units. The decoder is another LSTM network combined with local attention and consists of a single decoder LSTM layer with 256 hidden units. The latter is randomly initialized by the final state of theBiLSTM encoder to maintain long-term memory. The dense layer is a fully connected feed-forward network (FFN) that has equal input dimensionality. This dense layer produces the alignment scores between the encoder's hidden states and the previous decoder's hidden states. The model was trained using the Adam optimizer [33] with a batch size of 32 for 500 epochs. The MSE loss function is used and the dropout regularization has also been adopted to avoid overfitting. The learning rate is initialized at \(10^{-3}\). In our implementation, we use the NVIDIA GTX 1050 with CUDA of 10.1. The process is stopped when the validation loss does not refine for 10 epochs. To compare our experiments, we adopted five kinds of systems based on esophageal-to-laryngeal VC, which are JD-GMM, DNN, LSTM, BiLSTM, and Seq2 Seq with an attention mechanism. For training the JD-GMM, DNN, LSTM, and BiLSTM models, we used the DTW algorithm to time-align the parallel speech corpora. Note that to properly compare the performance, we took models with similar parameters. Thus, as a typical statistical approach, JD-GMM and DNN are considered as references. These methods are described as follows:  
* JD-GMM: the Joint Density GMM-based VC system was implemented based on the Sprocket toolkit introduced in VCC2018 [20] and considered as a baseline system. All the source and target parameters are directly estimated from the conversion function by the expectation-maximization (EM) algorithm. The source (\(x_{n}\)) and target (\(y_{n}\)) vectors previously aligned by the DTW algorithm are concatenated together into an extended vector \(z_{n}=[x_{n},y_{n}]^{\prime}\) and then the GMM parameters that model the joint probability density are estimated. * DNN: the DNN-based VC system was implemented based on the approach of [10]. The number of units at each layer is chosen in order to ensure the best network performance. The ReLU (Rectified Linear Unit) activation function was used for its good performance [34], the dropout was set to 0.5, the learning rate was 0.001, the batch size was 32, and the training epoch was set to 500. For synthesis, an overlap-add method was adopted to reconstruct the waveform of the estimated enhanced speech. * LSTM and BiLSTM: the LSTM and BiLSTM-based esophageal-to-laryngeal speech conversion models were implemented without an attention mechanism.