MINIMAX DESIGN OF ADJUSTABLE FIR FILTERS USING 2D POLYNOMIAL METHODS

The problem under study here is the minimax design of linear-phase lowpass FIR filters having variable passband width and implemented through a Farrow structure. We have two main contributions. The first is the design of adjustable FIR filters without discretization, using 2D positive trigonometric poly-nomials, an approach leading to semidefinite programming (SDP) formulation of the design problem. The second is to modify the design problem by a special choice for the pass-band and stopband edges of the variable FIR filter. The advan-tage is a lower implementation complexity. The new problem is solved using positive hybrid real-trigonometric polynomi-als and their SDP parameterization. Design examples prove the viability of our methods. Index Terms — adjustable FIR filters, positive polynomi-als, semidefinite programming 1