## 1 Introduction
However, there are no devices that make the diagnosis automatically, or that allow the identification of pathologies automatically. This manuscript contributes with an efficient algorithm for determination of autocorrelation, HNR, and NHR in order to develop devices using efficient algorithms to support the diagnosis of pathologies. Concerning the determination of harmonic parameters for voice analysis purposes, [PERSON] et al. in 1996 [24], compared fundamental frequency (\(f_{o}\)), jitter, shimmer and harmonics--or signal-to-noise ratio (HNR) measures made by commercially available acoustical analysis programs (CSpeech--Computer software working on DOS--Wisconsin, DC, USA, Computerized Speech Laboratory--PENTAX Medical--Hoya, Japan, SoundScope--Microsoft, and hand marking)--using a set of dysphonic voices. Measurements of HNR were demonstrated to receive a poor rank-order correlation between programs. Correlations between 0.4 and 0.6 resulted from the two-by-two comparison of the referred programs. The average HNR Hand marked with 21.31 dB received an average HNR of 8.58, 14.34, and 18.48 dB. This result showed very low consistency between commercial systems software to determine HNR. In signal processing, the Autocorrelation of a discrete time signal (or a time series) is the correlation of the signal with a lagged copy of itself as a function of the lag. The autocorrelation has maxima at lags equal to multiples of the fundamental period (T0 = 1/\(f_{\rm o}\)). The value considered in this work for the Autocorrelation parameter, in the context of speech signals, is the amplitude of the first peak after zero delays. Since the algorithm will be applied to quasi-periodic signals (voiced speech produced during the utterance of a vowel), this peak corresponds to the period of the quasi-periodic signal. It provides the identification of similar speech waveforms repeated throughout the signal. For the normalized Autocorrelation, this parameter can vary between 0 and 1, for white noise signals and periodic signals (harmonic component only), respectively. The Autocorrelation is very close to 1 (higher than 0.990) for normophonic voices and lower for dysphonic voices because normophonic voices uttering a vowel signal have mainly harmonic components (periodic) and very low noisy components (aperiodic). In contrast, dysphonic voices (depending on the pathology) tend to have lower harmonic components and higher aperiodic or noisy components. The HNR is a parameter in which the relationship between the harmonic and noisy components of a voiced speech segment indicates the general voice quality of the speech signal. The cyclic opening and closing of the vocal folds produce the harmonic components. The higher the HNR of a voiced signal, the higher the harmonic components, denoting normophonic behavior. It is common to find an HNR of over 20 dB in normophonic voices. There is no threshold value between normophonic and pathological voices, but there is a tendency for normophonic voices to have higher values and lower variance for HNR for the vowel /a/ (25,26). However, for vowel /u/, there is no statistical significance for different HNR between control and dysphonic voices, as shown in Figure 1 (right-hand side). As can be seen in Figure 1 (left-hand side), [PERSON] and [PERSON] (25) showed statistically significant higher values of HNR for the higher tone (higher \(f_{\rm o}\)) of the /a/ vowel than for normal and lower tones (lower \(f_{\rm o}\)). The same authors showed (Figure 1) statistically significant higher values of HNR for the vowel /u/ than for the vowel /a/. This difference evidences the dependency of the HNR on the sound and its structure concerning the frequency and energy of its formants. Figure 1: HNR along tones (h—high, l—low, n—neutral) for vowel /a/ (left-hand side), and along vowels (/a/,/i/, /u/) for neutral tone (right-hand side) for dysphonic and control voices. Groups are FD—Functional Dysphonia, HD—Hyperfunctional Dysphonia, PD—Psychogenic Dysphonia, D—Dysphonia and CG—Control Group.