Minimal multiplier realisation of bilinear-LDI digital allpass networks

Abstract

The paper outlines a procedure for the bilinear-LDI digital realisation of arbitrary-order stable analogue allpass transfer functions. The salient features of the resulting digital networks are (i) they are structurally allpass, i.e. their transfer functions are allpass independently of the specific choice of their multiplier coefficient values (ii) they are minimal in the number of digital multipliers required (iii) they require only one unit delay more than the minimum number possible. A comparison shows that, in terms of number of operations, these allpass networks are superior to the corresponding direct-form, direct-cascade-form and wave-digital realisations.