Frequency and voice: Perspectives in the time domain

Frequency variation is one of the most primitive features of voice production, endowing language and communication with richness and efficiency and enhancing enjoyment of the voice arts. In the first of two tutorial articles, the subject of frequency is examined formally, beginning in the time domain. A companion article explores the topic of frequency and voice from the frequency domain perspective. Frequency is a well-defined quantity of the sinusoidal function and of periodic functions of time. However, voice is inherently nonstationary, even over short time segments, to degrees that range from minor (stable vowels of a healthy voice) to major (singing voice and voiced consonants). For signals that are not periodic, the notion of frequency is ambiguous and often altogether unclear, which has led to a multitude of frequency-measurement techniques and discrepancy of measures. This article identifies the source of these discrepancies for a variety of time-domain techniques that are examined in the absence of noise. In the time domain, the subject of frequency is inherently coupled to the topic of signal modeling, which is explored in some detail. Sinusoidal models having time-varying phase are examined with the objective of achieving a frequency description of voice that is both continuous and instantaneous. The analytic signal method of mathematical physics is discussed and applied to the technology of empirical mode decomposition to demonstrate that the frequencies of voice may be comprehensively examined from the time domain point of view.