Design of stable 2-D recursive digital allpass filters using Hilbert transform

The allpass filter has the property of varying only phase with constant magnitude and it has mainly been used as a phase compensator for distorted signals. Among design methods for one-dimensional (1-D) allpass filters, the design method using the discrete Hilbert transform (DHT) has been proposed. The authors expand this to the two-dimensional (2-D) case for complex signals. However, in order to overcome the truncation problem, they approximate the discarded polynomial as a low order polynomial by employing Lagrange interpolation. As a result, all higher order coefficients than the one desired converge to zero, therefore, even after truncation, the stability can be guaranteed