NDLI: BIBO Stability of D-Dimensional Filters

Content Provider	Springer Nature Link
Author	Tomerlin, Andrew T. Edmonson, William W.
Copyright Year	2002
Abstract	Consider the class of d-dimensional causal filters characterized by a d-variate rational function $$H(z) = \frac{{P(z)}}{{Q(z)}}$$ analytic on the polydisk $$\mathbb{D}^d = \{ z = (z_1 , \ldots ,z_d ):\|z_i \| < 1\} $$ . The BIBO stability of such filters has been the subject of much research over the past two decades. In this paper we analyze the BIBO stability of such functions and prove necessary and sufficient conditions for BIBO stability of a d-dimensional filter. In particular, we prove if a d-variate filter H(z) analytic on $$\mathbb{D}^d $$ has a Fourier expansion that converges uniformly on the closure of $$\mathbb{D}^d $$ , then H(z) is BIBO stable. This result proves a long standing conjecture set forth by Bose in [3].
Starting Page	333
Ending Page	340
Page Count	8
File Format	PDF
ISSN	09236082
Journal	Multidimensional Systems and Signal Processing
Volume Number	13
Issue Number	3
e-ISSN	15730824
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2002-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Electronic and Computer Engineering Signal, Image and Speech Processing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Signal Processing Information Systems Computer Science Applications Software Hardware and Architecture

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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BIBO Stability of D-Dimensional Filters