A general synthesis procedure was developed by which matching sections can be synthesized. The values of the internal impedance of the generator and the load impedance can be given either in equation form or in the form of measurements. The synthesis procedure is based upon approximate solutions to the equations describing nonuniform transmission lines that have appeared in the literature. The matching problem is reduced to the problem of finding a real function, the reflection-distribution function, whose complex Fourier transform approximates a complex function, determined by the generator and load impedances. The reflection-distribution function must be identically zero outside a specified interval. The reflection-distribution function is found by expansion into a trigonometric series and subsequently determining the coefficients in this expansion. A method is developed by which the complex function to be approximated is first separated in real and imaginary parts. The coefficients in the trigonometric expansion are then determined such that these real and imaginary parts are approximated separately in a discrete Chebyshev sense (the maximum magnitude of the approximation error is minimum at a discrete number of sampling points). (Author).

found. Solution of the integral equation yields the function K(x,t) which determines U(x,(omega)) and, thus, Z(,0)(x). Also given is the extension of the theory to the case where both input and output discontinuities are present.