Introduction to Filter Concepts

Abstract

This introductory chapter lays the foundations of the book and it addresses those fundamental concepts and definitions which will be employed in later chapters. Thus, the magnitude frequency response is presented in the various forms encountered in practice such as plain gain, logarithmic gain and attenuation. Filters are then classified in the standard formats namely as lowpass, highpass, bandpass or band-reject according to their frequency responses and it is shown subsequently that ideal filtering characteristic versions of these cannot be realized by “real world” causal systems. In outlining the filter design procedure, it is demonstrated that that it can be simplified considerably by employing standard tools such as impedance and frequency scaling and normalization. Moreover to achieve a realizable and hence non-ideal filter response we need to resort to approximations, that is to say procedures for determining the appropriate mathematical gain functions which will satisfy a given set of gain specifications.