ABSTRACT
Derivatives, integrals, and weighted averages are examples of linear operations on random as well as on deterministic functions and data sequences. A practical implementation of a linear filter works in the time domain, changing the time course of a function. The theoretical analysis is however most conveniently performed in the frequency domain, where the effects of the filter is split on the different frequency components in the signal. It is perhaps fair to say that the spectral theory of stationary processes proves to be most useful in connection with linear filters. The formal and informal treatment of the spectral representation introduced in Chapter 3 considerably facilitates the derivation of the characteristics of a linear filter. This chapter deals with the general tools to handle covariance and spectral properties of linear filters. Special emphasis is given to the use of white noise in linear filters. Some special topics are treated in the next chapter.
