Design of Flat Halfband Filters With Sharp Transition and Differentiators through Constrained Quadratic Optimization

Abstract

An alternative method for the design of typeI Halfband FIR filters with flat magnitude and narrowtransition bands is presented. The methodology shownis based on the derivation of a quadratic programmingproblem with inequality constraints, which representsa set of linear equations obtained from flat and ripplerestrictions imposed over the frequency response of thefilter. The design is based on maximally flat constraints.The obtained filters have narrow transition bands ascompared to those presented in other maximally flatbased designs. The proposed method is not ripplefree as it does not take into account all the maximallyflat restrictions. Then, control of side lobes andtransition band is performed using a weighting matrixand inequality constraints as side lobes bounds. Thedesign of type IV FIR digital differentiators throughthe proposed method is also shown. Examples ofdesign, which compare the proposed method with otherspresented in the literature, are provided to verify theeffectiveness of the proposed method.