Linear filtering and piecewise linear correlation functions

For a class of piecewise linear correlation functions, it is shown that optimal linear mean-square filtering is achieved with a finite number of samples of the process for any finite observation interval. The class of correlation functions is defined by a particular property of the points at which they change slope. Conditions are discussed under which an arbitrary piecewise linear function is a correlation function. An example demonstrating various aspects of the theory is given, and applications of the theory are considered.