A generalized delay operator for shift-variant systems

This paper is concerned with the mathematical characterization of linear causal shift-variant systems when these systems are excited by causal inputs. Two fundamental concepts of shift-iavariant systems are generalized to the shift-variant case. The generalizations are in terms of linear differential operators. The transfer function is universalized to the transfer operator, and the delay z is extended to a linear differential operator called the generalized delay operator. Examples of both operators are included within the paper.