TABLE OF CONTENTS As indicated in the first chapter, an ideal filter is unattainable; the best we can do is to approximate it. There are a number of approximations we can use based on how we want to define "best." In this chapter we discuss four methods of approximation, each using a slightly different definition. Four sections are devoted to the major approximation methods used in analog filter design: the Butterworth, Chebyshev, inverse Chebyshev, and elliptic approximations. In each of these sections we determine the order of the filter required given the filter's specifications and the required normalized transfer function to satisfy the specifications. In the following section we discuss the relative advantages and disadvantages of using these approximation methods. But first we begin this chapter by describing analog filters mathematically in the form of linear system transfer functions.
An analog filter is a linear system that has an input and output signal. This system's primary purpose is to change the frequency response characteristics of the input signal as it moves through the filter. The characteristics of this filter system could be studied in the time domain or the frequency domain. From a systems point of view, the impulse response h( t) could be used to describe the system in the time domain. The impulse response of a system is the output of a system that has had an impulse applied to the input. Of course, many systems would not be able to sustain an infinite spike...
