## 4 Discussion  
Autocorrelation, HNR, and NHR were analyzed to understand if this efficient algorithm obtains values close to the reference values for control and pathological voices. The availability of an efficient algorithm allows the depruation of support diagnosis systems into hardware devices with lower computational power. Concerning the complexity of the proposed algorithm, it has a linear complexity behavior both in time and space. [PERSON]'s algorithm [PERSON] (1977) seems to have the same complexity level, but the proposed algorithm can be faster because of no overlapping requirement. Additionally, and according to the description of the Praat algorithm Praat (1977), it considers several peak candidates in the normalized Autocorrelation and takes the candidate in the voiced speech part with the highest value of the local strength, determined according to the rules defined (requiring additional calculus). In opposition, the method used in this algorithm straightly considers the peak as the highest value of the normalized Autocorrelation between 0.002 and 0.030 s (33 \(<\)\(f_{\mathrm{o}}\) \(<\) 500 Hz). This difference between the algorithms is acceptable because the Praat algorithm is adequate to be used with voiced and unvoiced parts of speech; meanwhile, the proposed algorithm is supposed to be used only with voiced speech parts of the signal. [PERSON], in 2009 [PERSON] et al. (2009), compared the measure of HNR in synthesized and pathologic human voices using time-, spectral-, and cepstral-based methods. The mean absolute errors for synthesized voices were 0.11, 0.52, and 0.61 dB for time- (using [PERSON]'s algorithm [PERSON] (1977)), spectral-, and cepstral-based algorithms using 100 Hz\(f_{\mathrm{o}}\) voices, respectively. For human pathologic voices, the HNR difference measured by the three methods was up to 1.93 dB for male voices and 3.68 dB for female voices. The author mentions a lower variation in time domain algorithms for different voices. The efficient algorithm presented in this manuscript has an average absolute difference of HNR of 0.26 (\(\sigma\) = 0.29) dB for pathological voices and 0.42 (\(\sigma\) = 0.23) dB for normophonic voices, compared to the same \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{HNR} & \multicolumn{4}{c}{Autocorrelation} \\ \cline{2-9}
**Samples** & \multicolumn{2}{c}{**Patients**} & \multicolumn{2}{c}{**Control**} & \multicolumn{2}{c}{**Patients**} & \multicolumn{2}{c}{**Control**} \\ \cline{2-9}  & **Ref.** & **Alg.** & **Ref.** & **Alg.** & **Ref.** & **Alg.** & **Ref.** & **Alg.** \\ \hline
1 & 32.86 & 30.75 & 15.03 & 13.64 & 0.998 & 0.998 & 0.942 & 0.935 \\
2 & 18.95 & 17.24 & 19.76 & 18.88 & 0.982 & 0.976 & 0.987 & 0.985 \\
3 & 19.14 & 18.40 & 20.04 & 19.10 & 0.985 & 0.983 & 0.989 & 0.986 \\
4 & 19.52 & 19.05 & 22.70 & 20.52 & 0.984 & 0.983 & 0.991 & 0.989 \\
5 & 24.50 & 23.06 & 25.21 & 22.24 & 0.994 & 0.993 & 0.995 & 0.992 \\
6 & 24.56 & 23.21 & 22.25 & 21.29 & 0.995 & 0.993 & 0.990 & 0.989 \\
7 & 18.34 & 17.17 & 18.44 & 16.23 & 0.983 & 0.979 & 0.977 & 0.972 \\
8 & 19.16 & 18.61 & 21.15 & 19.58 & 0.986 & 0.984 & 0.989 & 0.987 \\
9 & 14.78 & 14.68 & 23.03 & 20.04 & 0.955 & 0.953 & 0.992 & 0.987 \\
10 & 19.48 & 18.86 & 23.04 & 21.13 & 0.987 & 0.985 & 0.994 & 0.990 \\ Mean Abs. Difference & 1.03 (\(\sigma\) = 0.53) & 1.80 (\(\sigma\) = 0.66) & 0.002 (\(\sigma\) = 0.001) & 0.003 (\(\sigma\) = 0.002) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the values obtained by the algorithm with the reference software, for the parameters HNR and Autocorrelation, for the USP database. [PERSON]'s algorithm. The efficient algorithm presents results consistent with the best results in the literature. The differences in the efficient algorithm are also insignificant compared to the differences presented in [24], where the average HNR Hand marked with 21.31 dB received average HNR from commercial systems with a difference between 3 and 10 dB.