Stabilization and Stability Testing of Multidimensional Recursive Digital Filters
Mr. Niranjan Damera-Venkata
Laboratory for Image and Video Engineering
Dept. of Electrical and Computer Engineering,
The University of Texas at Austin
Austin, Texas
Monday, October 19, 1998, 12:30 PM, ENS 302
A recursive digital filter is defined to be BIBO stable, if every bounded input results in a bounded output. For causal one-dimensional (1-D) digital filters this condition can be shown to be equivalent to all poles of the filter transfer function lying within the unit circle in the complex plane. Stability testing thus reduces to evaluating the poles of the filter transfer function, and stabilization of unstable filters is achieved by reflecting the poles outside the unit circle into the unit circle.
The fundamental curse of multi-dimensional (M-D) digital signal processing is the lack of a factorization theorem. Thus, evaluating the poles of a multidimensional transfer function is generally not feasible. Stabilization techniques also have to be considerably different from the 1-D case.
In this lecture we will discuss the necessary and sufficient conditions for the stability of M-D recursive digital filters. Stability tests for M-D digital filters will be reviewed. In particular we will discuss the root map technique and cepstral methods, for quarter-plane filters and a linear mapping theorem for general non-symmetric half-plane filters. Stabilization techniques discussed will include Planar Least Squares Inversion (PLSI) and the Discrete Hilbert Transform (DHT).