Analog Filters

Abstract

In this chapter, we introduce the classical Butterworth, Chebyshev, Cauer, and Bessel filters which are intended to serve as the prototypes for the design of digital filters with related characteristics. For each of these types, the equations are derived to determine filter coefficients which meet the tolerance scheme of a desired frequency response. Some tables of filter coefficients can be found in the appendix which allow the filter design for a limited range of filter specifications. These, however, cannot replace commercially available filter design handbooks or filter design software. We start by considering low-pass filters as the prototypes for the design of digital filters. After the introduction of the characteristics of the ideal low-pass filter, we throw some light on the filter types named above, each of which is, in a certain sense, an optimum approximation of the ideal low-pass characteristic. Appropriate transformations allow the conversion of low-pass filters into high-pass, bandpass and bandstop filters with related characteristics. The corresponding transformation rules are also introduced in this chapter.