The Effects of Noise through an Analog Integrator Which Integrates with Respect to an Arbitrary Variable

A long-range investigation into the transmission, utilization, and processing of information for missiles and space vehicles has been initiated. The ultimate objective is a theory of control and communication for such vehicles which would relate the principles of information theory to the design philosophy of the control and communication systems. In investigating such information-theoretic guidance control problems, it is necessary to consider the effects of noise, both internal and external, on any possible computation control process. The external noises would arise in communication links, the drifts of gyros, possible variations in external conditions, variations in amounts and rates of rocket burning, and other causes. The internal noises could be those electronically generated (such as shot and Johnson noises) and those generated by digital computation processes. It is desirable to begin with simple but representative problems. In the event that an incremental digital or analog computer is part of a control loop, a typical problem would be signal plus noise into an analog or digital integrator.