Chebyshev Stopbands for CIC Decimation Filters and CIC-Implemented Array Tapers in 1D and 2D

The stopbands of a cascaded integrator-comb (CIC) decimation filter are ordinarily very narrow, as each results from a single multiple zero. Here response sharpening with a Chebyshev polynomial, using a previously reported CIC variant, separates each such multiple zero into an equiripple stopband. By trading unneeded depth at stopband center for improved depth at the stopband edge, the latter depth improves by some 6(N-1) dB in an Nth-order system. Increased computational complexity is modest: a few low-speed additions and multiplications by small integer coefficients that can often be chosen as powers of two. Alternatively, parameters can be configured to replace the many small stopbands with one large one, and this is demonstrated here with example spatial-processing CIC designs that create pencil beams for 1D and 2D receive antenna arrays.