Linear and quadratic methods for positive time-frequency distributions

This paper presents a new foundation for positive time-frequency distributions (TFDs). Based on an integral equation formulation of nonstationary systems, a positive TFD can be constructed from a decomposition of a signal over an orthonormal basis. This basis function definition of a positive TFD is used to obtain a relationship between the Wigner distribution and the positive TFD. The results are then generalized to derive positive joint distributions over arbitrary variables, following the approach of Baraniuk and Jones (1995). This general theory provides a common foundation for the two approaches of computing time-frequency representations: those based on linear decompositions of the signal (e.g. best basis methods) and those based on a quadratic, or bilinear, functional of the signal (i.e. Cohen's bilinear class).