ABSTRACT
Solution of the approximation problem is a major step in the design procedure of a filter and is equally important in the design of both analog and digital filters. It is through the solution of approximation problem that the filter designer determines the filter function, the response which satisfies the specifications. This chapter describes the characteristics of the permitted functions, and explains the approximation problem. It presents the best known and most popular functions used in the solution of the approximation problem for the required filter response in the frequency domain. Then, since these functions are lowpass, the chapter introduces suitable frequency transformations in order to obtain highpass, bandpass, or bandstop filters according to the requirements. In the case of magnitude approximation, the best known and most popular lowpass functions are the following: the Butterworth or maximally flat, the Chebyshev or equiripple, the monotonic or Papoulis, and the Cauer or elliptic function filters.
