Signal reconstruction from noisy, aliased, and nonideal samples: What linear MMSE approaches can achieve

This paper addresses the problem of interpolating a (non-bandlimited) signal from a discrete set of noisy measurements obtained from non-δ sampling kernels. We present a linear estimation approach, assuming the signal is given by a continuous model for which first and second order moments are known. The formula provides a generalization of the well-known discrete-discrete Wiener style estimator, but does not necessarily involve Fourier domain considerations. Finally, some experiments illustrate the flexibility of the method under strong noise and aliasing effects, and shows how the input autocorrelation, the sampling kernel and the noise process shape the form of the optimal interpolating kernels.