Optimum linear filtering of signals prior to sampling

A SOLUTION of the problem of determining a filter for the optimum recovery ¿ In a mean-square sense ¿ Of sampled data has been presented previously.1¿6 Examples for the application of this solution include radar tracking systems and systems where measuring instruments provided values at discrete time-instants. These are cases in which the data are available only in sampled form. However, there are important situations involving sampled data which are not included in this category. The case which is considered here is the one in which a continuous signal, consisting of data and noise, is to be sampled. In such a case, it is shown that the signal should be filtered before sampling. An expression is derived for the optimum ¿prefilter¿ as specified by a mean-square-error criterion, and examples are presented for illustration purposes.