ABSTRACT
This chapter introduces two of the most commonly used infinite impulse response (IIR) filters, the S. Butterworth and Chebyshev filters. These filters were invented in the form of continuous filters long before the advent of digital signal processing. The chapter describes lowpass version of each type of filter and shows how to convert these to digital lowpass IIR filters that are optimal in the same sense. For continuous filters, the stability requirement for continuous systems implies that s-plane poles must all be to the left of the imaginary axis, on the left half plane. The bilinear transformation, described by J. F. Kaiser and colleagues, is used to transform a continuous analog transfer function into a discrete digital transfer function and thus transform an analog filter into a digital filter. The spectrogram is an interesting application of the comb filter or any similar set of bandpass filters. Ordinary numerical operations like averaging and integration have existed since the dawn of civilization.
