Design of nonrecursive filters by specification of frequency-domain zeros

The problem of designing nonrecursive digital filters in the frequency domain consists of specifying a finite trigonometric polynomial which has "good" characteristics in the context of some application or criterion. Some current design procedures are indirect, in that the polynomial is specified via weighted time-domain sample values. In others, the polynomial is specified directly through its regular complex-amplitude samples. The method proposed here takes the zeros of the polynomial as its defining parameters. It is shown that the asymptotic attenuation rate of the filter can be controlled by adjusting the densities of the pass-band and stopband zeros, and that the "shape" of the filter can be adjusted through placement of specific zeros.