General results concerning the stability of 2-D digital filters with nonessential singularities of the second kind

✍ Scribed by L.M. Roytman; M.N.S. Swamy

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 735 KB
• Volume: 326
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(89)90073-2

✦ Synopsis

Previous results concerning the stability qf 2-D digital jilters in the presence of simple nonessential singularities of the second kind are extended to a very broad class of jiinctions having second kind singularities on T', the distinguished boundary of the unit bidisk, where these singularities may be simple or of multiple order. Necessary and suflcient conditions are given for the & and /,-stabilities and for the boundedness for a function of thet,vpeW,,z,) = P(zI,W{T Ql'(z,,zAi 14 z,, zz)}, where P/Q, has simple nonessential singularities of the second kind on T2. These conditions are computationally simple and are expressed in terms of multiplicities of the zeros of certain resultants of two-variable polynomials. Several examples are considered to illustrate the results.