On lossless digital 2×2 transfer functions that can be implemented with allpass transfer functions

Two-input-two-output digital filters that can be implemented with two scalar allpass transfer functions are obtained directly in the digital domain from lossless digital two-input-two-output transfer functions. The aim is to include allpass-based filters in the theory of 2×2 lossless systems and to extend known results in the literature. It is shown that mathematically the problem can be reduced to putting a special parameter matrix into the diagonal form. This observation is used to derive general conditions for the realization of a two-input-two-output lossless digital system with two scalar allpass circuits