BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Continuous-Time AR Model Identification: Does Sampling Rate Really Matter?

S. Maggio, H. Kirshner, M. Unser

Proceedings of the Eighteenth European Signal Processing Conference (EUSIPCO'10), Ålborg, Kingdom of Denmark, August 23-27, 2010, pp. 1469–1473.

We address the problem of identifying continuous-time auto regressive (CAR) models from sampled data. The exponential nature of CAR autocorrelation functions is taken into account by means of exponential B-splines modelling, allowing one to associate the available digital data with a CAR model. A maximum likelihood (ML) estimator is then derived for identifying the optimal parameters; it relies on an exact discretization of the sampled version of the continuous-time model. We provide both time- and frequency-domain interpretations of the proposed estimator, while introducing a weighting function that describes the CAR power spectrum by means of discrete Fourier transform values. We present experimental results demonstrating that the proposed exponential-based ML estimator outperforms currently available polynomial-based methods, while achieving Cramér-Rao lower bound values even for relatively low sampling rates. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/maggio1001.html,
AUTHOR="Maggio, S. and Kirshner, H. and Unser, M.",
TITLE="Continuous-Time {AR} Model Identification: {D}oes Sampling Rate
	Really Matter?",
BOOKTITLE="Proceedings of the Eighteenth European Signal Processing
	Conference ({EUSIPCO'10})",
YEAR="2010",
editor="",
volume="",
series="",
pages="1469--1473",
address="{\AA}lborg, Kingdom of Denmark",
month="August 23-27,",
organization="",
publisher="",
note="")
© 2010 EURASIP. 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 EURASIP. 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.