entia1 Weighting Algori nstruction of Bandlimited Signals
Miros € aw Pawlak, Adam Krzyżak · 1996
The problem of reconstruction of bandlimited signals from discrete, noisy observations is considered. Wbittaker-Shannon interpolation series-based estimates involving the weighting factors are proposed. It is shown that they converge as the sampling rate increases to infinity. The rate of convergence of the double exponential weighting algorithm is established. These results are corroborated in computer simulations. The aim of the present paper is to assess the performance of the WS reconstruction scheme in the presence of random errors. Unlike the previous papers, where only the point- wise truncation errors were considered, we study the mean integrated square error (MISE) properties of our algorithms. MISE analysis involves the bias and variance of reconstruction schemes, which we consider in detail. We first observe that direct application of the WS recon- struction algorithm to a signal sampled in the presence of noise leads to an infinite reconstruction error. Obviously, these are the most trying conditions that face the reconstruction In this context, the WS scheme is modified by first introduc- ing a new scheme based on exponential weighting. In deriving the algorithm, we follow the classical WS reconstruction scheme as closely as possible to obtain a scheme that would perform in the presence of noise and would not add too much complexity to the WS scheme. More sophisticated methods of variance reduction, using double smoothing, are also discussed in the paper. We refer also to (18), where multirate type