Synthesis of digital nonrecursive band-elimination filters for moving-target selectors

A synthesis of digital nonrecursive optimum Chebyshev band-elimination filters is shown, such filters of low order (n or = 4) being the simplest and thus most suitable for moving-target selection. They have an antisymmetric pulse response characteristic and a linear phase-frequency characteristic, their amplitude-frequency characteristic containing several equally large ripples in the stop band and one ripple in the pass band. The synthesis is based on a trigonometric polynomial derivable from an algebraic power polynomial by change of variables; sin (1/2 omega tau) becomes x. Such a filter can be designed for not less than the necessary attenuation in the stop band or for more than the allowable nonuniformity of the pass band. A filter of higher order becomes feasible upon widening the pass band so as that it will contain two or more ripples. This is demonstrated by the synthesis and design of a sixth-order filter in this class.