A Contribution to the Approximation Problem

A method is outlined whereby a given attenuation curve is approximated by the addition of a finite number of semi-infinite slopes, each of which in turn is closely approximated by the attenuation curve of a Butterworth function. These functions therefore constitute a set of approximation functions for impedance functions. The set is extended by the addition of Tschebyscheff functions, which seem more appropriate for the approximation of curves with filter properties. The method avoids most of the labor normally involved in the numerical solution of approximation problems and the calculation of impedance zeros and poles. It seems especially suited for cases of rather smooth attenuation curves extending over a wide range of frequency. A short indication is given of how to apply the same method to the approximation of resistance, reactance, and phase functions.