Time normalization of voice signals using functional data analysis

The harmonics-to-noise ratio (HNR) has been used to quantify the waveform irregularity of voice signals [Yumoto et al., J. Acoust. Soc. Am. 71, 1544-1550 (1982)]. This measure assumes that the signal consists of two components: a harmonic component, which is the common pattern that repeats from cycle-to-cycle, and an additive noise component, which produces the cycle-to-cycle irregularity. It has been shown [J. Qi, J. Acoust. Soc. Am. 92, 2569-2576 (1992)] that a valid computation of the HNR requires a nonlinear time normalization of the cycle wavelets to remove phase differences between them. This paper shows the application of functional data analysis to perform an optimal nonlinear normalization and compute the HNR of voice signals. Results obtained for the same signals using zero-padding, linear normalization, and dynamic programming algorithms are presented for comparison. Functional data analysis offers certain advantages over other approaches: it preserves meaningful features of signal shape, produces differentiable results, and allows flexibility in selecting the optimization criteria for the wavelet alignment. An extension of the technique for the time normalization of simultaneous voice signals (such as acoustic, EGG, and airflow signals) is also shown. The general purpose of this article is to illustrate the potential of functional data analysis as a powerful analytical tool for studying aspects of the voice production process.