New Designs of MAXFLAT FIR Halfband Low/High Pass Digital Filters with Narrow Transition Bands

MAXFLAT FIR digital filters has the smoothest and the most accurate magnitude responses among all the available types of FIR digital filters. However, the transition bands of MAXFLAT filters are relatively wider, and this makes them unattractive in certain applications. Traditionally, low/high pass MAXFLAT FIR filters are designed to satisfy MAXFLAT constraints at ends of the frequency band. In this paper, we present two new designs of halfband low/high pass filters that satisfy these constraints at the middle of the pass and stop bands. The first design is obtained by solving a system of linear equations obtained by applying MAXFLAT constraints to the magnitude response of the filter, while the second design is a transformation of one of our previous designs of maximally linear digital differentiators. Design examples show that the transition bands of the presented designs are narrower as compared to traditional designs