## 3 Results
### Sensitivity to the Sampling Frequency Variation  
In order to test how the algorithm behaves in the determination of Autocorrelation and HNR with the variation of the sampling frequency, the same sounds were decimated (resampled) from the original 50 kHz to the sampling frequency of 25 kHz and 12.5 kHz. The decimation process intends to reduce the original sampling frequency. An antialiasing digital low-pass filter preceded the decimation process. The Chebyshev Type I of order 8 was used. For this analysis, the same method was used for the original signal with 50 kHz to determine the best window and glottal period. However, in this case, only the Hanning window with six glottal cycles was used since this window and length obtained the best results for the two parameters previously. Table 2 presents a similar analysis as previously, now only with the Hanning window and six glottal cycles, but for 25 kHz and 12.5 kHz. The HNR and Autocorrelation values obtained by the algorithm for these sampling frequencies were compared with the reference value for the signal with 50 kHz (original signal). The comparison also consists of determining the average of the individual sample differences (90 samples for each group). The data in Table 2 show a slight increase in the HNR differences in the value measured by the algorithm compared to the values obtained with the sampling frequency of 50 kHz. This increase is more accentuated for Fs of 12.5 kHz. For the Autocorrelation, the results are similar to those obtained with the sampling frequency of 50 kHz. There is an insignificant variation in the patients and control subjects for 25 kHz and 12.5 kHz. Then, the mean and standard deviation of all HNR values determined by the algorithm and the reference software for the three values of sampling frequency were compared. Table 3 shows the average HNR considering all control subjects and patients, for the nine audio samples per subject (180 samples in total), with the Hanning window and six glottal cycles in the algorithm. Through the analysis of Table 3, it is possible to observe that the HNR for the values of the algorithm varies with the sampling frequency and has a maximum variation of 2.04 dB. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sampling Frequency (kHz)**} & \multicolumn{4}{c}{**Average Difference**} \\ \cline{2-5}  & \multicolumn{2}{c}{**HNR (dB)**} & \multicolumn{2}{c}{**Autocorrelation**} \\ \cline{2-5}  & **Patients** & **Control** & **Patients** & **Control** \\ \hline
25 & 0.58 (\(\sigma=0.38\)) & 1.16 (\(\sigma=0.33\)) & 0.006 (\(\sigma=0.005\)) & 0.001 (\(\sigma=0.001\)) \\
12.5 & 2.03 (\(\sigma=0.32\)) & 3.45 (\(\sigma=0.63\)) & 0.006 (\(\sigma=0.006\)) & 0.004 (\(\sigma=0.002\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: HNR and Autocorrelation average differences as a function of sampling frequency. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sampling Frequency (kHz)**} & \multicolumn{2}{c}{**HNR (dB)**} & \multicolumn{2}{c}{**Autocorrelation**} \\ \cline{2-5}  & **Algorithm** & **Reference** & **Algorithm** & **Reference** \\ \hline
50 & \
\begin{tabular}{c} 23.89 \\ (\(\sigma=2.56\)) \\ \end{tabular} &
\begin{tabular}{c} 24.02 \\ (\(\sigma=2.32\)) \\ \end{tabular} & 0.981 (\(\sigma=0.009\)) & 0.984 (\(\sigma=0.007\)) \\ \hline
25 & \
\begin{tabular}{c} 22.98 \\ (\(\sigma=2.59\)) \\ \end{tabular} &
\begin{tabular}{c} 23.85 \\ (\(\sigma=2.49\)) \\ \end{tabular} & 0.980 (\(\sigma=0.010\)) & 0.984 (\(\sigma=0.007\)) \\ \hline
12.5 & \
\begin{tabular}{c} 21.85 \\ (\(\sigma=2.55\)) \\ \end{tabular} &
\begin{tabular}{c} 24.59 \\ (\(\sigma=2.33\)) \\ \end{tabular} & 0.980 (\(\sigma=0.010\)) & 0.984 (\(\sigma=0.007\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: HNR and Autocorrelation as a function of the sampling frequency. The Autocorrelation has a slight variation since the difference along Fs is 0.001 for the algorithm and 0.004 comparing the algorithm with the reference value.