DESIGNING FIR FILTERS WITH GLOBALLY MINIMAX-OPTIMAL MAGNITUDE RESPONSE

摘要

Embodiments of the present disclosure provide mechanisms that enable designing an FIR filter that would have a guaranteed globally optimal magnitude response in terms of the minimax optimality criterion given a desired weight on the error in the stopband versus the passband. Design of such a filter is based on a theorem (“characterization theorem”) that provides an approach for characterizing the global minimax optimality of a given FIR filter h[n], n=0, 1, . . . , N, where optimality is evaluated with respect to a magnitude response of this filter, |H(e^jω)|, as compared to the desired filter response, D(ω), which is unity in the passband and zero in the stopband. The characterization theorem enables characterizing optimality for both real-valued and complex-valued filter coefficients, and does not require any symmetry in the coefficients, thus being applicable to all non-linear phase FIR filters.