Biorthogonal partners and applications

Two digital filters H(z) and F(z) are said to be biorthogonal partners of e ach other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as fi lterbank theory, exact and least squares digital interpolation, and multire solution theory They also play a central role in the theory of equalization , especially fractionally spaced equalizers in digital communications. In t his paper, we first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal part ners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of th e above-mentioned applications.