Difference equation implementation of time-variant digital filters

Abstract

Certain researchers derive the time-variant transfer function of a digital filter by assuming its behavior at certain sampling points. Based upon the derived coefficients, the transfer function is implemented via a time-variant difference equation by assuming a "frozen-time" relationship between the transfer function and its difference equation. This paper derives the generalized transfer function for a class of time-variant difference equation and illustrates the difference between the frozen-time and the generalized transfer functions.