A technique using Jacobian elliptic functions is given which by removing a previous method's (Powell and Chau, 1991) double-zero constraint, yields improved designs of linear phase IIR filters.>

Symmetry conditions are derived for the amplitude and phase response of vestigial-sideband (VSB) filters. A design technique, based on Szentirmai's frequency transformation, is described for the realization of filters which automatically satisfy these symmetry relations. The synthesis can be carried out with either thesor thez(transformed frequency) variable. It is shown that for sharply selective VSB filters the delay distortion exhibits an even symmetry around the carrier frequency. The equalization of loss and phase distortions can thus be easily carried out in the baseband. A typical design problem is described and solved to illustrate the effectiveness of the suggested synthesis technique.