Optimum crossing-point estimation of a sampled analog signal with a periodic carrier

Authors:
Graeme Smecher;Benoít Champagne
Affiliations:
Department of Electrical and Computer Engineering, McGill University, Canada;Department of Electrical and Computer Engineering, McGill University, Canada
Venue:
Signal Processing
Year:
2011

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Abstract

The problem of estimating the crossing points of a continuous-time random process, represented by a sequence of uniformly spaced noisy samples, with a periodic analog carrier signal is of crucial importance in the implementation of pulse-width modulation (PWM) and other event-triggered sampling systems. In this paper, we formally approach this problem from a statistical signal processing perspective under a Bayesian framework. We derive the maximum a posteriori (MAP) estimator of the crossing point from a finite sequence of noisy observations, along with a close approximation based on minimum mean squared error (MMSE) considerations. We also study the Bayesian Cramer-Rao bound (CRB) on attainable mean square estimation error. Finally, simulations of a PWM scenario demonstrate that both the MAP and MMSE estimators approach the CRB and outperform several benchmark estimators. The MMSE is a particularly attractive solution as it offers a computationally efficient approximation to the MAP estimator.