Authors : E. Morris Abraham Gnanamuthu and P.S. Reddy
Abstract: In this paper we have provided a complete solution for the classical unsolved problem of stability of the Planar Least Squares Inverse (PLSI) polynomials. One positive thing we have proved is that if the given 2-D polynomial and its PLSI polynomial are of the same degree being less than or equal to two, the PLSI polynomial is always stable. Other thing is if the coefficient matrix [A] of the given polynomial is centro-symmetric or symmetric, the PLSI polynomial may be unstable if the degree of the PLSI polynomial is greater than or equal to three. It is observed that if the matrix [A] has no relationship whatsoever among its coefficients, then the PLSI will be stable even for degrees greater than or equal to 3. We then looked into the counter examples available in the literature and provided reasons for the occurrence of instability of the PLSI polynomials. We have provided enough examples to strengthen our results.
E. Morris Abraham Gnanamuthu and P.S. Reddy , 2004. The PLSI Method of Stabilizing 2-D Recursive Digital Filters-A Complete Solution . Asian Journal of Information Technology, 3: 628-641.