Single‐Input/Output Relationships
Julius S. Bendat, Allan G. Piersol · Wiley series in probability and statistics · 2010
This chapter is concerned with the theory and applications of input/output relationships for single-input problems. It is assumed that records are from stationary random processes with zero mean values and that systems are constant-parameter linear systems. Single-input/single-output (SI/SO) models and single-input/multiple-output (SI/MO) models are discussed. Ordinary coherence functions and optimum frequency response functions are defined for these models. Models formulated are appropriate for studying the properties of multiple transmission paths between a single source and different output points. It is assumed that constant-parameter linear systems can be used to describe these different possible paths and that all unknown deviations from ideal cases can be included in uncorrelated extraneous output noise terms. The chapter also considers the removal of extraneous noise with illustrations to determine the signal-to-noise ratios and the spectral densities of the signals in the three output measurements. Controlled Vocabulary Terms coherence; frequency response function; input/output process; mean values; random process; spectral density function; white noise