EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Unified Theory


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Vers une théorie unificatrice pour le traitement numérique/analogique des signaux

M. Unser

Plenary talk, proceedings of the Twentieth GRETSI Symposium on Signal and Image Processing (GRETSI'05), Louvain-la-Neuve, Kingdom of Belgium, September 6-9, 2005, pp. 557-558.



We introduce a Hilbert-space framework, inspired by wavelet theory, that provides an exact link between the traditional—discrete and analog—formulations of signal processing. In contrast to Shannon's sampling theory, our approach uses basis functions that are compactly supported and therefore better suited for numerical computations. The underlying continuous-time signal model is of exponential spline type (with rational transfer function); this family of functions has the advantage of being closed under the basic signal-processing operations: differentiation, continuous-time convolution, and modulation. A key point of the method is that it allows an exact implementation of continuous-time operators by simple processing in the discrete domain, provided that one updates the basis functions appropriately. The framework is ideally suited for hybrid signal processing because it can jointly represent the effect of the various (analog or digital) components of the system. This point will be illustrated with the design of hybrid systems for improved A-to-D and D-to-A conversion. On the more fundamental front, the proposed formulation sheds new light on the striking parallel that exists between the basic analog and discrete operators in the classical theory of linear systems.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser0508.html,
AUTHOR="Unser, M.",
TITLE="Vers une th{\'{e}}orie unificatrice pour le traitement
        num{\'{e}}rique/analogique des signaux",
BOOKTITLE="Twentieth {GRETSI} Symposium on Signal and Image Processing
        ({GRETSI'05})",
YEAR="2005",
editor="",
volume="",
series="",
pages="557--558",
address="Louvain-la-Neuve, Kingdom of Belgium",
month="September 6-9,",
organization="",
publisher="",
note="{Plenary talk}")

© 2005 GRETSI. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from GRETSI.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.