Design of Maximally-Flat and Monotonic FIR Filters using the Bernstein Polynomial

Abstract

This paper presents a recently introduced technique for the design of Maximally-flat (MAXFLAT) FIR filters by using the Bernstein polynomial, and reviews its applications in (i) establishing the equivalence between the earlier known methods, and (ii) formulating a matrix approach for determining the coefficients of MAXFLAT FIR filters efficiently. We also review a new, optimal design procedure for MAXFLAT filters and extend the method to generate monotonic FIR filters with arbitrary magnitude specifications, for which, presently, no method exists. Further, these concepts have been used here to design Quadrature Mirror Filters (QMF) with extremely low reconstruction error.

Indexing terms:

• Digital filters
• Maximally-fiat FIR filters
• Monotonic FIR filters
• Quadrature mirror filters