A stochastic process model of sound program signals
Shiro Ehara · 2005
A product-structured stochastic processU(t)=V(t)\cdotW(t)is proposed for a model of sound program signals and a general pdf (probability density function) ofU(t)is derived from the pdfsg(v)andh(w)of the respective component processesV(t)andW(t). The structure of the model gives a kind of statistical properties of orchestra music sounds as follows; the pdfh(w)of fluctuating rms-valued intensityW(t)follows the M-pdf, the pdfg(v)of the audible componentV(t)=U(t)/W(t)follows the Gaussian pdf, and the pdff(u)ofU(t)may be expressed in an integral representation. The respective cdfs (cumulative distribution functions)F(u)andH(w)ofU(t)andW(t)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.