On the convergence properties of the simple hyperstable adaptive recursive filter (SHARF)

In previous work the authors have developed a class of provably convergent adaptive algorithms for digital IIR filters based on the concept of hyperstability. While this class of adaptive filters offers much promise in practical applications little has been done toward providing the characterization that would allow a designer to select filter order, adaptation constants, and other design parameters. This paper reports on the initial effort toward providing this information through an investigation of the local convergence behavior of SHARF, the simple hyperstable adaptive recursive filter.