An application of analog computers to the statistical analysis of time-variable networks

IN RECENT years an extensive body of mathematical techniques has been developed for the analysis of the response of linear constant coefficient control systems to stationary random processes as inputs. In many cases it is possible to achieve direct synthesis of the optimum system for an assigned task. For nonstationary inputs or variable coefficient systems, no corresponding theory exists, even though problems of this nature arise quite often in practice. In the present paper an analog method is presented for the rms error analysis of a class of nonstationary problems. However, no attempt is made at the synthesis of an optimum system. Following a brief discussion of analog methods applicable to the general nonstationary case, our attention is concentrated on the special problem of a variable coefficient linear system with a stationary random input. Exploitation of the properties of the adjoint system in this case is shown to reduce considerably the labor in computing rms errors in comparison with the general method for nonstationary inputs. The simulation of the adjoint system is shown to be readily obtainable from the simulation of the original system.