An origin of statistical formulations of speech signals

Summary form only given, as follows. In the 1960s, Fant G. and others developed a concrete formant theory of speech production using both physiological and engineering approaches. These classical and deterministic concepts laid one firm foundation tool for speech processing of today. In the mid 1960s, we introduced a statistical or stochastic concept in speech analysis, reconstruction, coding and recognition. This induced quite a few speech analysis method, such as MLES (the maximum likelihood estimation of speech spectrum), PARCOR (partial correlation) analysis/synthesis, LSP (line spectrum pair), and CSM (composite sinusoidal modelling); they have been fully developed and expanded to all aspects of speech processing by many researchers and have formed the essential methods for speech processing of the last century. I introduce the early development of statistical formulations of speech signals, based on the mathematical and statistical theory of stochastic processes, which were developed by Kolmogrorof, Wiener, Cramer, Wold, Grenander, Whittle, Robinson, Burg, Akaike, etc, during 1930s through 1960s. I also mention the works of Szego, Levinson, Geronimus, etc, whose pure mathematical results played very significant role in the development of these methods. I express a wish that similar situations may break out again in the speech processing fields, by making use of contemporary pure and applied mathematics.