Some comparisons of approximation techniques in the design of delay-equalised selective filters

Abstract

A novel technique is first presented for construction of the transfer functions of selective filters satisfying stringent magnitude and group-delay specifications in the passband. The passband loss is minimised in terms of a least-mean-square norm, while the complex attenuation poles are adjusted iteratively so as to obtain an equal ripple approximation to a constant group delay over the largest portion of the passband. This technique, referred to as the unconstrained least-mean-square approximation, is then compared with the most commonly used method of designing delay-equalised filters with the Chebyshev passband-magnitude characteristic. Another recently introduced technique for determining non-minimum-phase transfer functions is which the passband magnitude response is constrained to be a monotonic function of frequency is also discussed. As revealed by numerical examples, the unconstrained least-mean-square approximation compares favourably with the approximation methods in which the passband magnitude response is constrained to be either a Chebyshev or a monotonic function of frequency.