A stochastic process model of sound program signals

A product-structured stochastic process is proposed for a model of sound program signals and a general pdf (probability density function) of is derived from the pdfs and of the respective component processes and . The structure of the model gives a kind of statistical properties of orchestra music sounds as follows; the pdf of fluctuating rms-valued intensity follows the M-pdf, the pdf of the audible component follows the Gaussian pdf, and the pdf of may be expressed in an integral representation. The respective cdfs (cumulative distribution functions) and of and showed good agreement not only with the measured cdfs of orchestra sounds but also with the various kinds of measured cdfs of sound program signals including speech signals. A concise table is given for the representation of measured distributions with shape parameters, instead of ordinary graphical presentation.