Filtering with Convex Response Constraints
The envelope constrained (EC) filtering problem has been outlined in Chapter 1 as a constrained optimization problem in Hilbert space, where the filter’s response to a prescribed signal is required to stay inside a given envelope. In this chapter, we introduce a convex programming problem in Hilbert space, which covers all digital, analog and hybrid filter design problems of interest in this monograph. The formulation considers the general case where all filter responses to a bounded set of excitations are constrained to a closed and convex set. This abstraction is developed to address a wide range of EC filtering problems in a unified manner. An important result is the convergence of the costs of feasible and finite dimensional solutions to the optimal cost. This allows optimum filters to be approximated by realizable filters that satisfy the constraints.
KeywordsImpulse Response Feasible Region Finite Impulse Response Finite Impulse Response Filter Input Noise
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