CHAPTER 7
Multiple-Input/Output Relationships
Material contained in Chapter 6 is now extended to multiple-input problems. As before, all data are assumed to be from stationary random processes with zero mean values, and all systems are constant-parameter linear systems. Section 7.1 describes multiple-input/single-output (MI/SO) models for general cases of arbitrary inputs and for special cases of mutually uncorrelated inputs. These ideas are discussed for special cases of two-input/one-output models in Section 7.2. Optimum frequency response functions, and partial and multiple coherence functions are defined for these models. Iterative computational procedures to decompose MI/SO models into physically meaningful ways are presented in Section 7.3, based upon original ideas in Refs 1 and 2. A practical modified procedure with simpler notation is recommended in Section 7.4, with details given for cases of three-input/single-output models. Results for multiple-input/multiple-output (MI/MO) models are stated in Section 7.5 using a matrix formulation. Many engineering applications of Ml/SO procedures for different fields are in Refs 2 and 3.
7.1 MULTIPLE-INPUT/SINGLE-OUTPUT MODELS
Consider q constant-parameter linear systems Hi(f), i = 1, 2,…, q, with q clearly defined and measurable inputs xi(t), i = 1, 2,…, q, and one measured output y(t), as illustrated in Figure 7.1. There is no requirement that the inputs be mutually uncorrelated. The output noise term n(t) accounts for all deviations ...
