Insights into digital filters made as the sum of two allpass functions

The exact equivalence of the response of a resistance terminated lossless analog lattice filter to that of the algebraic sum of two allpass functions is discussed, culminating in a theorem giving simple necessary and sufficient conditions for a transfer function to be realized in this way. It is shown how various basic analog circuit relationships and properties possess direct counterparts in the realm of digital filtering. The importance of using the well-known characteristic function of analog filter theory for designing digital filters as the sum or difference of two allpass functions is emphasized.>