Digital filter design using root moments for sum-of-all-pass structures from complete and partial specifications

This paper is concerned with the development of digital filter design procedures for transfer functions in the form of sum-of-all-pass in which the requirements may be partially specified. Specifically, the requirements for a digital filter or equalizer in amplitude A(θ), or phase φ(θ), or possibly group-delay response τ(θ), may be specified from measurements over a limited a set of frequencies {θ₁,θ₂}. The problem is to develop techniques for the design a transfer function H(z) satisfying these specifications and constrained to be in the form of a sum-of-two-all-pass functions. The proposed solution is based on the use of root moments. The companion problem concerned with the estimation of the orders of the required all-pass filters is also examined and a solution proposed based on the same context of root moments.