Abstract
Two-dimensional (2D) recursive digital filters find applications in image processing as in medical X-ray processing. Nonsymmetric half-plane (NSHP) filters have definitely positive magnitude characteristics as opposed to quarter-plane (QP) filters. In this paper, we provide methods for stabilizing the given 2D NSHP polynomial by the planar least squares inverse (PLSI) method. We have proved in this paper that if the given 2D unstable NSHP polynomial and its PLSI are of the same degree, the PLSI polynomial is always stable, irrespective of whether the coefficients of the given polynomial have relationship among its coefficients or not. Examples are given for 2D first-order and second-order cases to prove our results. The generalization is done for theth order polynomial.
Highlights
The two-dimensional (2D) filters find numerous applications like in image processing, seismic record processing, medical X-ray processing, and so forth
We deal with the problem of stabilizing unstable nonsymmetric half-plane (NSHP) 2D recursive filters by the planar least squares inverse (PLSI) approach
We dealt with the stabilization of 2D NSHP polynomials by the PLSI approach
Summary
The two-dimensional (2D) filters find numerous applications like in image processing, seismic record processing, medical X-ray processing, and so forth. We deal with the problem of stabilizing unstable NSHP 2D recursive filters by the planar least squares inverse (PLSI) approach. Genin and Kamp [3] were the first to give a counterexample showing that the Shanks conjecture, which says that 1D technique of stabilizing can be extended to 2D case, fails They have taken the original unstable 2D polynomial to be of degree three in both the variables, and the corresponding PLSI polynomial of degree one was found to be unstable. In [8], a new method of stabilizing multidimensional (N > 2) recursive digital filters has been presented This new method boils down to the same DHT method when applied to 1D and 2D filters.
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