The Approximation Problem of Network Synthesis

The approximation problem of network synthesis is surveyed with extensive reference to the recent literature, encompassing both the frequency and the time domains. The topics reviewed include the concept of complex frequency, approximation by point-coincident polynomials, and the Fourier series method. Butterworth functions for maximally flat approximation and Tchebycheff polynomials for equal-ripple approximation inside the pass band are treated, as well as Jacobian elliptic functions which provide Tchebycheff behavior both inside and outside the pass band. A detailed review of the literature of the potential analog is given with reference to applications of the analogy and to the use of electrolytic tanks and rubber sheets. Men- tion is made of continued fractions and Laguerre polynomials to- gether with references to papers discussing the synthesis of networks with prescribed transient response. A bibliography of 240 items is included.