An algorithm to evaluate the L∞norm for some common filters

The L
∞
norm is used in some algorithms to determine the ordering of the pole-zero sections of cascade digital filters. This note develops simple expressions that easily evaluate the L
∞
norm entirely in the Z-domain for filters having zeros on the unit circle (i.e., Butterworth, Chebyshev, and elliptic digital filters designed using the bilinear Z-transformation).