Showing papers on "Network theory published in 1984"

Lossless inverse scattering, digital filters, and estimation theory

Abstract: Methods to construct rational solutions of the lossless inverse scattering (LIS) problem for one-port passive digital systems are described. The first method is recursive and can be viewed as a generalization of the celebrated Schur algorithm. The second method is global and leads to a parametrization of what we call fundamental solutions from which all LIS solutions may be constructed. Quite a few classical problems in estimation theory and network theory may be viewed as special cases of the LIS problem. With each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process.

Some applications of graph theory to network analysis and synthesis

Abstract: This paper describes applications of graph theory to some of the problems of network analysis and synthesis, starting with the early days of network theory. The first section is devoted to the classical results related to the topological analysis of linear, passive, and transfornerless networks. Then it goes over to contributions dealing with generalization of these methods to networks with mutual couplings and active elements. Appearance of integrated circuits and digital computers provided both motivation and means for studying large-scale systems. A part of the paper is devoted to publications on large-scale network analysis dealing with diacoptics and graph theoretic methods for defining efficient Gaussian elimination algorithms for solution of sparse sets of linear algebraic equations. The part on topological synthesis starts with the early results dealing with relations between the structure and the properties of passive, reciprocal networks without mutual inductances. The last section is devoted to contributions in the field of topological synthesis of pure resistive networks dealing with such topics as conditions of realizability, minimal realizations and bounds on the number of port-terminals.

Interests and Knowledge

Abstract: The careful reader will have noted our use of the term ‘interest’ at a number of places in earlier chapters and will rightly have concluded that this concept plays an important role in the network theory of knowledge. The purpose of the present chapter is to elaborate upon this notion. We may start by recalling that we talked, earlier, of the ‘workability’ or ‘utility’ of networks and argued that this is the acid test of the success thereof. If a network allows the individual to interact satisfactorily with his or her environment, then it is upheld and reinforced. If, on the other hand, the behaviour of the environment is unpredictable from the standpoint of the network (as in the case of Xaanthi and his notion of ‘mammal’ or the child and the parrot) then this network is undermined and susceptible to change. However, in order to judge network workability, the individual has to ask questions of it. The network is not an idle set of terms disconnected from reality. It is a tool that may be used when the individual is trying to achieve a goal or solve a problem. It is an instrument, fashioned for certain purposes. It is a resource that allows the individual to move from A to B in his or her environment. It is, as we saw, like a map that will serve certain interests and not others.

Activities on Network Theory and Circuit Design in Europe

Abstract: Many basic ideas in the development of network theory and methods for circuit design originated from European scientists and en- gineers. In this paper we give a short survey of some essential activities in Europe on the theory and design of continuous and discrete-time analog networks during the last half century. The topics included are realizability theorems, reactance two-port synthesis, filter design, transmission-line networks, circuit analysis and simulation.

Activities on network theory and circuit design in Europe

Abstract: Many basic ideas in the development of network theory and methods for circuit design originated from European scientists and engineers. In this paper we give a short survey of some essential activities in Europe on the theory and design of continuous and discrete-time analog networks during the last half century. The topics included are realizability theorems, reactance two-port synthesis, filter design, transmission-line networks, circuit analysis and simulation.

The Lossless Inverse Scattering Problem in the Network-Theory Context

Abstract: We present the theory leading to a theorem that describes all the rational solutions of the lossless inverse scattering problem (LIS-problem) for lossless networks. They are parametrized by a set of points in the closed unit disc of the complex plane. Quite a few classical problems in estimation theory and network theory may be viewed as a special case of the LIS problem. We present a global method to construct LIS solutions using reproducing kernel Hilbert space methods. Finally, we give connections with applications and with some classical interpolation problems and relate the results to maximum entropy approximation theory.