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In this paper, we propose a method for encoding continuous-time Gaussian signals subject to a usual data rate constraint and, more importantly, a reconstruction delay constraint. We first apply a Karhunen-Loève decomposition to reparameterize the continuous-time signal as a discrete sequence of vectors. We then study the optimal recursive quantization of this sequence of vectors. Since the optimal scheme turns out to have a very cumbersome design, we consider a simplified method, for which a numerical example suggests that the incurred performance loss is negligible. In this simplified method, we first build a state space model for the vector sequence and then use Bayesian tracking to sequentially encode each vector. The tracking task is performed using particle filtering. Numerical experiments show that the proposed approach offers visible advantages over other available approaches, especially when the reconstruction delay is small.