Sampling of noisy signals: Spectral vs anti-aliasing filters

In the paper we study the properties of sampling stochastic signals corrupted by a wideband stochastic noise where samples are taken either directly from resulting signal, or as the output from a continuous-time filter. We consider two types of filters: anti-aliasing filters whose characteristics depend solely on sampling period, and Kalman filters, whose characteristics depend on spectra of signals of interest.We also study possible improvement attained by discretetime Kalman filtering applied to the sampled signal. We compare the results of two competitive methods: classical point-wise sampling followed by discrete-time filtering, and continuous-time filtering prior to sampling possibly followed by digital filtering. The study is performed for a wide range of sampling periods and noise-to-signal ratios and leads to important practical conclusions.