Two Design Techniques for Digital Phase Networks

The increasing availability of digital signal processors such as those described in Refs. 1 and 2 has generated much interest in the algorithmic design of digital filters. One particular class of recursive digital filters commonly referred to as all-pass digital networks has an important and interesting design problem associated with it. That is, the design objective for this type of filter involves the following transfer function £ H{z~x) = ^ N *=0 bN-kz~k · L bkz~k Because of the relationship between numerator and denominator polynomials, the number of degrees of freedom in filter design has been reduced to N from the usual 2N. Since the magnitude function of H(z~l) is precisely 1.0 on the unit circle, the design problem is focused directly on the phase variation of H(z~l). The importance of this design problem does not arise from an academic viewpoint. There are signal processing applications in which an influential factor in signal fidelity is the amount of phase distortion present in 767