Second order systems for filtering and sampling methods

This paper presents some invariance properties of differential equations, used for generating truncated test-function (functions which differ from zero only on a certain interval and with only some derivatives f(1), f(2), ..f(n) continuous on the real axis). The functions are used for the multiplication of some received signals, in order to take into account the random variations of the integration period of these signals, the integration being proportional to the mean value of the signal. Such fluctuations are generated by the switching phenomena at the end of the integration. The paper presents also the properties of second order oscillating systems, considered as generating "practical" (i.e. truncated) test functions (PTF), in filtering and sampling procedures.