The Phase Characteristics for the Stability of 2-D Nonsymmetric Half-Plane Digital Allpass Filters
Ju-Hong Lee, Jiun-Shian Du · IEEE Transactions on Circuits and Systems I Regular Papers · 2016
The phase-response property for the bounded-input bounded-output (BIBO) stability of a two-dimensional (2-D) causal recursive digital allpass filter (DAF) with nonsymmetric half-plane (NSHP) support region is presented. Both cases of filters with real coefficients and complex coefficients are explored. Moreover, the effect of the numerator polynomial of a 2-D NSHP DAF on stability is also considered. The presented phase-response property has several applications. A remarkable application is that it can be utilized to enforce stability for a 2-D NSHP DAF design by choosing an appropriate phase specification. The eigenfilter design of 2-D NSHP DAFs for this application is also presented. Design examples are given to show these applications and the stability of a 2-D NSHP DAF is also inspected by the 2-D spectral factorization-based algorithm and a zeros-examining method presented by Ekstrom and Woods for confirmation.