Some considerations in the design of multiband finite-impulse-response digital filters

Although much has been learned about the relationships between design parameters for finite impulse-response (FIR) low-pass digital filters, very little is known about the relationships between the parameters of multiband filters. Thus given a set of design specifications for a multiband FIR filter (e.g., filter band edge frequencies and desired ripples in each of the bands) it is difficult to choose a set of modified parameters which will yield an acceptable filter using a standard FIR design algorithm. By an acceptable filter we mean one with monotonic behavior of the frequency response in the DON'T-CARE or transition regions between bands and one providing at least the desired attenuation (or ripple) in each of the bands. In this paper, we examine the theoretical and practical issues of designing multiband filters and present several strategies for choosing the input parameters for the McClellan et al. filter-design algorithm to yield reasonable filters which meet arbitrary specifications.