On Half-Band, Third-Band, and Nth-Band Fir Filters and Their Design

Abstract

Half-band FIR digital filters are known to be important due to their reduced computational requirements. They are especially valuable when used to decimate or interpolate by a factor of 2 [1], where their characteristics well match the filtering requirements. Computational savings can also be achieved by extending the concept of half-band filters to Nth-band filters for use in decimation or interpolation by a factor of N. In this paper, it is shown that for certain filter requirements, common to decimation and interpolation, an Nthband filter exists with passband and stopband ripples only slightly larger than those of the optimal FIR filter. It is demonstrated that optimal half-band filters can be designed by using the computer program of McClellan, Parks, and Rabiner [2]. It is also shown that useful Nthband filters can be designed by using this program, which is perhaps the most widely available filter design program. Copyright © 1982 by The Institute of Electrical and Electronics Engineers, Inc.