Understanding and Using the Spectral Density Matrix

Dr. Marcos Underwood, Tony Keller, Spectral Dynamics, Inc.

Abstract:
In several current areas of Engineering which are seeing quite a bit of activity, the Spectral Density Matrix (SDM) has assumed an increasingly important role. Whether it relates to Multi-shaker vibration testing, MIMO, or Multi-Reference Frequency Response Function measurements, the SDM forms an important role in understanding and controlling dynamic structural responses.

This paper will review the Spectral Density Matrix and discuss the importance of creating and updating this Matrix in real-time. Practical examples of using this matrix will be given and applications both in Measurement and control will be explored. The SDM is both a Hermitian and a nonnegative definite matrix. These properties can have very important practical and physical interpretations. Their use will be explored, for example, in the context of multiple, stationary, Gaussian, partially correlated Random drive signals creating measured Acceleration response signals on complex structures. The importance of Phase and Coherence in the practical application of these matrices and on the Cross Spectral Density Matrix will also be reviewed.

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