Considerations of Linkages between Analog and Digital for Function x(n)

This paper describes a method of hybrid computation for the problems including the function x(n). And the greater part of it is devoted to the considerations of the linkages between the analog and the digital for the function x(n). Here the function x(n) appears frequently in the form of x(2) or x(4) in the industrial problems. As is well known the function x(2) is the characteristic included in fluid-flow problems, and x(4) is in heat-radiation problems. The weak points of analog computation for these characteristics are in accuracy and stability, but can be compensated by making use of digital computer for these parts. In the industrial uses the exclusive digital computer is more convenient than the general-purpose one. Here the relative error of analog computation, the linkages, the number of the digital elements and their relationships are considered at the same time and as the results the reasonable method of hybrid computation is obtained. That is, the exclusive digital multiplier with a compressor and an expandor is found reasonable. Its design considerations are described in details, but it is the basic idea among others that the characteristics of the compressor and the expandor are determined so that the relative error of the signal appearing at the output of the latter may be constant and as the results the necessary and sufficient number of the digital elements may be decreased. And in practice these characteristics are also realized approximately by a group of the straight lines through the origin. Finally the reduced rate of the digital elements and the optimum condition of the approximation are illustrated together with an example.