## 4 Experiments
### Function Verifications  
This subsection verifies the function of the VHLS implementation. The experiments are conducted by the CUEB French Phoneme Database 1.0 established by the Capital University of Economics and Business and the Institute of Acoustics CAS [27], which includes 35 phonemes \(\times\) 6 sessions \(\times\) 23 participants \(=\) 4830 samples. The participants in the data collection are asked to read the French phonemes shown in Table 3 six times to perform six different data sessions. \begin{table}
\begin{tabular}{l l} \hline \hline
**15 Vowels** & \\ \hline Vowel: & [a], [i], [e], [c], [y], [u], [0], [3], [0], [0], [0] \\ Nasal vowel: & [3], [5], [6] \\ \hline
**3 semi vowels** & [j], [w], [u] \\ \hline
**17 consonants** & \\ \hline Deaf consonants: & [p], [t], [k], [f], [s], [l] \\ Sound consonants: & [b], [d], [g], [v], [2], [3] \\ Lateral consonants: & [l], [r] \\ Nasal consonants: & [m], [n], [g] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: French phoneme table. Figure 6 shows the test bench of the experiments. The preprocessing cycles of the input phoneme waveform include band filtering, Fourier transforming, and normalizing. The normalized frequency spectrum is used as the predictor vector for the detectors. We verify the functions of the proposed implementation (\(capt\_vhls\)) by comparing it with its Matlab prototype (\(capt\_matlab\)) and C++ routine (\(capt\_cpp\)). Moreover, in order to evaluate the diagnostic error rate of the selected algorithm, the PLS regressor (\(pls\_matlab\)), hard-margin SVM (\(hmsvm\_matlab\)), soft-margin SVM (\(smsvm\_matlab\)), and deep neural network (\(dnn\_matlab\)) are implemented in Matlab as references. All the reference implementations are specified in Table 4. All the implementations are considered to be constructed by input, hidden, and output layers. The hidden layer numbers of \(capt\) implementations and \(dnn\_matlab\) are two and three, and those of the other implementations are one. The lost value and maximal iteration number are set as \(1\times 10^{-6}\) and \(1000\), respectively. The ReLU and sigmoid functions are used as the activate functions of \(dnn\_matlab\). Considering that machine learning modules necessitate high data precision and the values of speech signals usually have a large dynamic range, the data type of the proposed implementation is set to floating-point one. We also tried to use the fixed-point data to realize the same function and found that all the threshold values must be carefully set if the similar accuracy performance are desired. That is, fixed-point implementation may lead to unknown risks in the case of this paper. We divide the data set into two groups for training and testing, each with different size ratios. The size ratios are \(R\) = 1:5, 2:4, 3:3, 4:2 or 5:1. The average diagnostic error rate of \begin{table}
\begin{tabular}{l l l} \hline \hline \multirow{2}{*}{**Implementations**} & **Layer Sizes** & \multirow{2}{*}{**Descriptions**} \\  & **(Input/Hidden/Output)** & \\ \hline \(pls\_matlab\) & 16,384/16,384/1 & \
\begin{tabular}{l} Matlab implementation of PLS \\ regressor \\ Matlab implementation of \\ hard-margin SVM \\ Matlab implementation of \\ soft-margin SVM \\ Matlab implementation of \\ neural network \\ Matlab prototype of \\ Algorithm 2 \\ \end{tabular} \\ \(capt\_cpp\) & 16,384/16,384/64/1 &
\begin{tabular}{l} C++ routine of Algorithm 3 \\ VHLS implementation of \\ Algorithm 2 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Implementation specification I.  
Figure 6: Testbench of the proposed phoneme diagnostic IP cores. three measurements is used to determine the final evaluation result. Figure 7 compares the diagnostic error rates of all the implementations. First, it demonstrates that the diagnostic error rates decrease with the increases in the training set size. This is because enough training data improves the machine learning classifiers by overcoming the over-fitting problems.