On restoring band-limited signals

The problem of reconstruction of band-limited signals from discrete and noisy data is studied. The reconstruction schemes employing cardinal expansions are proposed and their asymptotical properties are examined. In particular, the conditions for the convergence of the mean integrated squared errors are found and the rate of convergence is evaluated. The main difference between the proposed reconstruction scheme and the classical one is in treating differently the sampling rate and the reconstruction rate. This distinction is necessary to ensure consistency of the reconstruction scheme in the presence of noise.