Statistical errors in measurement of coherence functions and input/output quantities

Abstract

Practical statistical error analysis formulas are developed for evaluating ordinary, partial and multiple coherence function estimates, and associated quantities which occur in analysis of single input/output problems and in multiple input/output problems. These include estimates of coherent output spectra and estimates of gain and phase factors of related frequency response functions. Models are either single input/output models or conditioned input/output models, where the latter models can be created from arbitrary measured multiple input/output data. Guidelines are presented to reduce statistical errors in such computed quantities. These results are essential for applications to identify different multiple noise sources, to determine multiple system properties, to measure response effects due to the sources acting singly or in various combinations, to simulate multiple random environments, and to predict system failures from response measurements only.