Criteria to select kernel functions for positive time-frequency distributions of theoretical time-varying signals

The development of positive time frequency distributions (PTFD) is an important issue in the framework of time frequency analysis of nonperiodic signals. A PTFD can be interpreted as the signal energy localized in both time and frequency domains. A PTFD representation depends on a kernel function which is related to the signal to be analyzed. For any particular signal, it is difficult to know its PTFD by only using time and frequency marginal distributions. We show that the uncertainty coefficient based on the entropy principle is a good approach to deciding which kernel function could be appropriate for analyzing a set of sinusoidal signals. As well, a lower bound of the uncertainty coefficient was defined based on the marginal product (correlationless case of PTFD). Three known kernel functions were used to calculate the PTFD of six sinusoidal signals. These signals were considered as a simple approximation to oscillation changes in the electrical activity of the human colon. One of the kernel functions was useful for analyzing almost all sinusoidal signals