NATURE AND USE OF LIMIT-CYCLES IN DETERMINING THE BEHAVIOR OF CERTAIN SEMIDETERMINATE SYSTEMS

For some well‐known systems such as speech encoders or digital filters, the excursions of the input are so dramatic and so loosely correlated that the system performance itself appears indeterminate. For these systems we present a technique of determining the system behavior by feeding a set of coherent frequency signals. For the analog inputs of any such system, we derive these inputs from coherent frequency synthesizers all synchronized to a common signaling frequency. For digital inputs into the system, we derive these inputs from a single master clock and set of logic functions to yield the desired bit patterns at different input ports. We present experimental evidence of the existence and utilization of these limit cycles for systems with some initial knowledge about the configuration and interconnections of components. The techniques presented here do not apply to systems for which complete initial ignorance is asserted. © 1979 The Bell System Technical Journal