Design of digital filters with maximally flat passband and equiripple stopband magnitude
T. Saramäki · International Journal of Circuit Theory and Applications · 1985
Abstract This paper introduces a general class of digital filters with maximally flat passband magnitude, equiripple stopband magnitude, and different order numerator and denominator. the classical Chebyschev type II (inverse Chebyschev) filters having equal numerator and denominator orders are considered as special members of this filter class. the filter types to be considered are lowpass, highpass and bandpass. the proposed filter class consists both of filters having all the zeros on the unit circle and of filters having some zeros off the unit circle to contribute to the passband shaping. An efficient iterative algorithm for the design of filters of the given type is presented. It is based on shaping the passband and stopband responses alternately until the difference between successive solutions is within given tolerance limits. Several comparisons show that in wideband applications filters with numerator order higher than denominator order present considerable advantages over equivalent Chebyschev type II designs, in terms of multiplication rate and/or frequency selectivity. In narrowband applications, in turn, filters with higher denominator order are shown to be the most effective.