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

Abstract

Abstract-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 ( ), or phase ( ), or possibly group-delay response ( ), may be specified from measurements over a limited a set of frequencies 1 2 . The problem is to develop techniques for the design a transfer function ( ) 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.

A New Method for Design of Selective Digital Iir Filters With Arbitrary Phase

“…As a consequence, total approximation error is influenced only by phase approximation error of the all-pass sub-filter H 1 (z). Therefore, the resulting filter will have the elliptic magnitude characteristic, taking into account the straightforward relationship between the magnitude of selective filter and phases of all-pass sub-filters, given by (5) and (7). In case of the arbitrary shape phase, the all-pass function H 0 (z) approximates the desired phase () in whole frequency band   [0, ].…”

“…Besides mentioned standard structures for filter implementation, selective filter could be also realized by two all-pass sub-filters connected in parallel [7][8][9] (see Fig. 1).…”