Digital filters with prescribed zeros

We discuss the design of digital filters with maximally flat or equiripple passband behavior and transfer functions of the form
H(z)= K \frac{(z+1)^{q}\Pi\min{i=1}\max{r}(z-e^{j\omega_{i}})(z-e^{-j\omega_{i}})}{D_{n}(z)}
, where q+2r, the number of finite-plane zeros, is allowed to vary from 0 to n, the filter order. Analytic expressions are given for the magnitude squared function. Identification of the stopband edge frequency is treated in detail. The hard-ware requirements of these filters are compared with those of Chebychev and elliptic designs.