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A generalized spectral-analytical method (GSAM) for analyzing data of various physical nature has been developed. It is based on the generalized Fourier representation of the original experimental and model digital arrays. In this report, it is used in the implementation of a resonant-impedance method for diagnosing and studying the characteristics of mechanical systems (in particular, linear one-dimensional acoustic systems with local anomalies). In the framework of this approach, the anomaly (damage) of the syst...