Flat magnitude response FIR halfband low/high pass digital filters with narrow transition bands

MAXFLAT FIR low/high pass digital filters are traditionally designed to satisfy the constraints of maximal flatness at the ends of the frequency band. In this paper, we show that by moving the points of flatness to the inner band, halfband filters with narrow transition bands can be realized. This, however, affects the smoothness of their magnitude responses at the ends of the frequency band. We propose a new design of halfband filters having their points of flatness at the middle of the pass and stop bands. The resulting filters have significantly narrow transition bands as compared to the existing MAXFLAT designs, and yet their magnitude responses are quite smooth in the entire frequency band.