Recursive synthesis of linear time-variant digital filters via Chebyshev approximation

The present paper investigates the recursive realization of a rational generalized transfer function (GTF) as a linear time-variant (LTV) difference equation. We develop a relationship between a GTF and a time-variant difference equation. The unique realizability of a GTF as a LTV difference equation is discussed. Procedures for determining a timevariant difference equation from a given GTF having constant coefficients in its denominator are then developed. For a GTF having time-variant coefficients in its denominator, a "best" approximate realization is numerically determined based on the Chebyshev norm to minimize the residual vector.