Book excerpt: In Chapter 1, using the differential equation as the fundamental system description, we show how to obtain the filtering functions associated with physical systems; namely, the impulse response, step response, weighting function, and convolution integral. Chapter 2 introduces the Fourier and Laplace transforms, which lead to the frequency-domain system descriptions including the transfer function, magnitude response, phase response, and group-delay response. An introduction to the Hilbert transform, which is useful for relating specific network functions. In chapter 3 theoretical and realizable lowpass responses, including limitations in the time and frequency domains, are discussed. In Chapter 4 we concentrate on the transformation of the normalized lowpass prototype into other filter types. The narrowband and bandpass filter is discussed in detail because its analysis is applicable to crystal, helical, coaxial cavity, stripline, interdigital, and waveguide filters. In chapter 5 we consider the all-pass function, a function that is useful for phase and group delay equalization and for the simulation of specified delay. In chapter 6 we discuss the finite Q elements and predistortion. In chapter 7 we switch the focus from classical filter treatment to a consideration of the filtering of signals in a noisy environment, in particular, the matched filter. In chapter 8 we discuss the two methods of time-domain synthesis, the quasi-stationary approach to the analysis of linear systems excited by modulated inputs, and the subject of average time delay. Chapter 9 is devoted to digital filtering and includes a discussion of the z-transform