Direct design of sharp cutoff low-pass recursive digital filters

Effects of introducing single or multiple zero pairs on the unit circle on the all-pole transitional Butterworth-Chebyshev filter transfer function are investigated. It is shown that, for the same order n, a filter with zeros on the unit circle provides much sharper cutoff than all-pole filters. Coefficients of the magnitude squared function are given in a closed form. Graphs, helpful in designing such filters, are plotted.