Integral Representation of Zero-Memory Nonlinear Functions

Integral representation of zero-memory nonlinear functions has been extensively used by Bennett, Rice and others (see References) in the solving of problems such as the finding of modulation products when one or more sinusoids appear at the input, and the finding of the output autocovariance function when sine wave and random noise are applied. In relation to the necessary calculations which occur in the use of these integral representations, a class of functions known as Bennett functions, after W. R. Bennett, has been defined. A selected representation of these functions has been tabulated and plotted. While the original studies were carried out in relation to problems encountered in communications, the methods and the results can certainly be applied to advantage in control problems. Some work in this regard has been done by J. C. Lozier in unpublished notes on the analysis of the oscillating control servomechanism. On the whole, however, it appears that, these approaches are not known to investigators in the controls field. The present paper represents an attempt to summarize in a unified manner the work that has been done and to indicate the 1813