An Application of the Barrett-Lampard Expansion to Obtain the Slope Characteristics of a Speech Signal

Many methods of speech waveform encoding utilize differential techniques for bandwidth compression. The channel bit rate of these systems is directly related to the slope characteristics of the speech signal. Employing well-known statistical characteristics of speech, this paper presents a derivation of the probability density function (pdf) for the differential slope of a speech signal and evaluates two families of pdfs. The technique used here, based on the Barrett-Lampard expansion, can also be applied to the general problem of obtaining the pdf of a random signal that has been digitally filtered. In this way, the frequency reliance upon a Gaussian assumption can be avoided.