Design of flat halfband filters with sharp transition and differentiators through constrained quadratic optimization

Platas Garza, Miguel Ángel y Rodríguez Maldonado, Johnny (2017) Design of flat halfband filters with sharp transition and differentiators through constrained quadratic optimization. Computación y Sistemas, 21 (2). pp. 293-303. ISSN 1405-5546

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Resumen

An alternative method for the design of type I Halfband FIR filters with flat magnitude and narrow transition bands is presented. The methodology shown is based on the derivation of a quadratic programming problem with inequality constraints, which represents a set of linear equations obtained from flat and ripple restrictions imposed over the frequency response of the f ilter. The design is based on maximally flat constraints. The obtained filters have narrow transition bands as compared to those presented in other maximally flat based designs. The proposed method is not ripple free as it does not take into account all the maximally f lat restrictions. Then, control of side lobes and transition band is performed using a weighting matrix and inequality constraints as side lobes bounds. The design of type IV FIR digital differentiators through the proposed method is also shown. Examples of design, which compare the proposed method with others presented in the literature, are provided to verify the effectiveness of the proposed method.

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