An Introduction to Random Processes for the Spectral Analysis of Speech Data

Spectral analysis of acoustic data is a common analytical technique with which phoneticians have ample practical experience. The primary goal of this paper is to introduce to the phonetician, whose primary interest is the analysis of linguistic data, a portion of the theory of random processes and the estimation of their spectra, knowledge of which bears directly on the choices made in the process of analyzing time series data, such as an acoustic waveform. The paper begins by motivating the use of random processes as a model for acoustic speech data, and then introduce the spectral representation (or, spectrum) of a random process, taking care to relate this notion of spectrum to one that is more familiar to phoneticians and speech scientists. A final section presents two methods for estimating the values of the spectrum of a random process. Specifically, it compares the commonly-used (windowed) periodogram to the multitaper spectrum, and it is shown that the latter has many beneficial theoretical properties over the former