On designing sharp cutoff low-pass filters

Effects of introducing single or multiple pairs of coincident
j\omega
axis zeros in all-pole Chebyshev filter transfer functions are investigated. It is shown that for the same order
n
, Chebyshev filters with finite
j\omega
axis zeros provide much sharper cutoff than all-pole Chebyshev filters. It is also shown that for the same
n
, the same number of pairs of zeros
m
, and the same locations of zeros, the cutoff slope and stopband characteristic of the finite zero Chebyshev filters are much better than those of the finite zero Butterworth filters. Graphs helpful in the design of such filters have been plotted and their use is illustrated by an example.