Design of sharp-cut-off low-pass filters with ripples in the pass-band

For the design of sharp-cut-off low-pass filters, derived from all-pole Chebyshev filters, one needs to determine n, the order of the filter; m, the order of finite zeros; ¿0, the location of the zeros; and ¿, the ripple controlling factor, from the required specifications of cut-off slope, tolerable pass-band deviation, minimum acceptable attenuation in the stop-band and any other desirable constraints. The information with regard to cut-off slope and partial results with regard to stop-band tolerance are already available; the present paper gives the other necessary details in respect of pass-band as well as stop-band performances. The pole positions are also tabulated for some low orders; permissible allowed values of m; ¿0 ranging from 1.01 to 2.00; and one representative value of ¿.