Abstract
A general filter design norm is proposed with the intent of producing a unified design algorithm for all types of filters - FIR, IIR and 2D FIR with complex specifications. The Chebyshev, least squares, and constrained least squares problems become special cases because this norm uses a convex combination of the 2-norm and the Chebyshev norm. The primary benefit of this new problem formulation is that a single efficient multiple exchange algorithm (similar to Remez) has been developed to cover all the different filter types for magnitude and phase approximation. In the new algorithm, a small subproblem is formed at each step and is solved with an iterative reweighted least squares technique which can handle the design of complex filters easily. Finally, the norm definition allows easy trade-offs between the relative importance of error energy and worst-case error.
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