Accurate Short-term Analysis of the Fundamental Frequency and the Harmonics-to-noise Ratio of a Sampled Sound

We present a straightforward and robust algorithm for periodicity detection, working in the lag (autocorrelation) domain. When it is tested for periodic signals and for signals with additive noise or jitter, it proves to be several orders of magnitude more accurate than the methods commonly used for speech analysis. This makes our method capable of measuring harmonics-to-noise ratios in the lag domain with an accuracy and reliability much greater than that of any of the usual frequency-domain methods. By definition, the best candidate for the acoustic pitch period of a sound can be found from the position of the maximum of the autocorrelation function of the sound, while the degree of periodicity (the harmonics-to-noise ratio) of the sound can be found from the relative height of this maximum. However, sampling and windowing cause problems in accurately determining the position and height of the maximum. These problems have led to inaccurate timedomain and cepstral methods for pitch detection, and to the exclusive use of frequency-domain methods for the determination of the harmonics-to-noise ratio. In this paper, I will tackle these problems. Table 1 shows the specifications of the resulting algorithm for two spectrally maximally different kinds of periodic sounds: a sine wave and a periodic pulse train; other periodic sounds give results between these. Table 1. The accuracy of the algorithm for a sampled sine wave and for a correctly sampled periodic pulse train, as a function of the number of periods that fit in the duration of a Hanning window. These results are valid for pitch frequencies up to 80% of the Nyquist frequency. These results were measured for a sampling frequency of 10 kHz and window lengths of 40 ms (for pitch) and 80 ms (for HNR), but generalize to other sampling frequencies and window lengths (see section 5). Periods per window Pitch determination error ∆F/F Resolution of determination of harmonics-to-noise ratio sine wave pulse train sine wave pulse train > 3 < 5·10–4 < 5·10–5 > 27 dB > 12 dB > 6 < 3·10–5 < 5·10–6 > 40 dB > 29 dB > 12 < 4·10–7 < 2·10–7 > 55 dB > 44 dB > 24 < 2·10–8 < 2·10–8 > 72 dB > 58 dB