Optimal Design of Filters for Multirate Systems

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Parks The objective of this research is to develop procedures for the design of optimum multirate digital filters. The criterion used for optimality is derived from the norm of a linear operator that represents the filter. When applied to the design of linear, time-invariant filters this measure of optimality reduces to the usual Chebyshev frequency domain error criterion. For multirate-systems, this approach leads to a new criterion for filter optimality. This provides a quantitative, analytic design procedure that yields better filters than intuitive design methods that are in common use. The methods for the development of appropriate error functions use techniques from singular value decomposition and analysis of periodically time-varying linear systems. The development of efficient design algorithms is based on semi-infinite programming and Remez-like multiple exchange methods. This research is expected to establish limits for performance of multirate filters as well as to provide improved filters. Present designs can be compared with the best attainable to determine possible improvements.