Open Access

A Unified Transform for LTI Systems—Presented as a (Generalized) Frame

  • Arie Feuer1,
  • Paul M.J. Van den Hof2 and
  • Peter S.C. Heuberger2
EURASIP Journal on Advances in Signal Processing20062006:091604

https://doi.org/10.1155/ASP/2006/91604

Received: 19 August 2004

Accepted: 31 May 2005

Published: 20 February 2006

Abstract

We present a set of functions in and show it to be a (tight) generalized frame (as presented by G. Kaiser (1994)). The analysis side of the frame operation is called the continuous unified transform. We show that some of the well-known transforms (such as Laplace, Laguerre, Kautz, and Hambo) result by creating different sampling patterns in the transform domain (or, equivalently, choosing a number of subsets of the original frame). Some of these resulting sets turn out to be generalized (tight) frames as well. The work reported here enhances the understanding of the interrelationships between the above-mentioned transforms. Furthermore, the impulse response of every stable finite-dimensional LTI system has a finite representation using the frame we introduce here, with obvious benefits in identification problems.

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Authors’ Affiliations

(1)
Department of Electrical Engineering, Technion-Israel Institute of Technology
(2)
Delft Center for Systems and Control, Delft University of Technology

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Copyright

© Feuer et al. 2006