Design of a class of multirate systems using a maximum relative ℒ2-error criterion

A criterion for designing the class of multirate systems for rate changing is presented. This criterion arises from a model-matching perspective with maximum relative L²-error over a general class of inputs and is a natural extension of the standard Chebyshev method for filter design. Using multirate and convex analysis techniques, the criterion is shown to lead to a convex matrix-valued-function approximation problem. An algorithm using convex optimization is proposed to solve the problem. An example illustrates the use of the algorithm and effectiveness over standard filter-design techniques