Wavelet analysis of experimental data: Some methods and the underlying physics

As a generalization of time-frequency analysis, wavelet methods combine sequential and spectral discrimination with pattern recognition. In conjunction with conventional statistical tools of time series analysis, these features are at the basis of new ways to characterize experimental data. The methods presented in this paper can be formulated as sequences of modular algorithms that characterize and/or enhance specific features of dynamical interest, and can be compared with specialized post-processing instrumentation. The investigator plays an important role in matching the wavelet-based algorithms to specific data, much in the same way as he/she selects instrumentation. The feedback between the physical insight and the implementation of new algorithms characterizes this phase of the research. In this paper, a toolbox is presented with illustrative examples.