On half-band, third-band, and Nth-band FIR filters and their design

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 Nth-band 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 Nth-band filters can be designed by using this program, which is perhaps the most widely available filter design program.