A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >

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Time-frequency distributions-a review

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided. >

Linear and quadratic time-frequency signal representations

Past, present and future of nonlinear system identification in structural dynamics

Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples

Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

J.K. Hammond

Papers

Higher-order spectra: the bispectrum and trispectrum

The analysis of non-stationary signals using time-frequency methods

The interpretation of the bispectra of vibration signals—: I. Theory

Parameter estimation for hysteretic systems

The interpretation of the bispectra of vibration signals—: II. Experimental results and applications