The design of FIR filters in the complex plane by convex optimization

Abstract The design of FIR filters in the complex domain is performed by complex Chebyshev approximation where the continuous complex approximation problem is considered as a convex semi-infinite programming problem. This approach permits the filter design under (in)finitely many additional convex constraints on the system function of the filter. For the solution of the semi-infinite programming problem a new method is presented which can be interpreted as a further development of the well-known Kelley-Cheney-Goldstein cutting plane method for finite convex programming. This method is simpler and as reliable as the authors' method in [30, 31], the only other method until now which likewise has proved convergence and can solve continuous design problems with constraints. Filters designed by the method are presented, in particular one with 1000 coefficients. For a number of test examples the method is compared with that in [30, 31].

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