Complex principal oscillation pattern analysis

Abstract

The approach used here results from a critical review of the theory of linear systems of first order. It turns out that these systems cannot appropriately model standing oscillations. The notion of the traveling rate of a mode is defined, and it is demonstrated that the mode's frequency and traveling rate are directly coupled via the system matrix. One consequence is that clean standing oscillations cannot be modeled by linear systems of first order. CPOP analysis introduces a new vector of state. By defining the complex state "state + i.momentum,' both the conventional state itself and its momentum are simultaneously described. The method is capable of resolving oscillatory patterns of any given traveling rate from a stationary process. First experiments show that the CPOPs evolve more regularly and with less noise than corresponding POPs. -from Author