Time series response data from harmonic tests can be resolved into real and imaginary components. In comparing two signals, one phased relative to the other, the real and imaginary model coefficients of the relative signal represent components that are in phase with the reference signal and 90° out-of-phase, respectively. Obtaining these real and imaginary components is a well understood process. However, determining the quality of the component estimates requires the use of a statistical technique known at the multiple multivariate delta method. In this paper, the delta method is described in the context of estimating real and imaginary components to response signals. This development includes a brief review of the multiple linear regression techniques used to analyze the excitation and response signals individually. Additionally, the delta method is verified by comparing estimated variances with variances obtained in a Monte Carlo simulation. The results of this analysis can be applied to experimental structural dynamics modeling and to the problem of updating finite element models. In both of these cases, use of the delta method provides statistically optimal weightings to the least-squares formulations used in these modeling techniques.
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