Filtering Aspects of Practical Test-Functions and the Ergodic Hypothesis

Abstract

This papers presents properties of dynamical systems able to generate practical test-functions (defined as functions which differ to zero on a certain interval and possess only a finite number of continuous derivatives on the whole real axis) when the free-term of the differential equation (corresponding to the received input signal) is represented by alternating functions. The shape of the output signal (obtained by numerical simulations in Matlab based on Runge-Kutta functions) is analyzed, being shown that for high-frequency inputs an external observer could notice (in certain condition) the generation of two different pulses corresponding to two distinct envelopes. Such as aspect differs to the oscillations of unstable type second order systems studied using difference equations.