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

  • Arie Feuer
  • Paul M.J. Van den Hof
  • Peter S.C. Heuberger
Open Access
Research Article
First Online:
  • 652 Downloads
Part of the following topical collections:
  1. Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory

Abstract

We present a set of functions in Open image in new window 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.

Keywords

Information Technology Identification Problem Impulse Response Quantum Information Generalize Frame 
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Copyright information

© Feuer et al. 2006

Authors and Affiliations

  • Arie Feuer
    • 1
  • Paul M.J. Van den Hof
    • 2
  • Peter S.C. Heuberger
    • 2
  1. 1.Department of Electrical EngineeringTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands

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