Multiscale analysis and modeling using wavelets

Measured data from most processes are inherently multiscale in nature owing to contributions from events occurring at different locations and with dif ferent localization in time and frequency. Consequently, data analysis and modeling methods that represent the measured variables at multiple scales a re better suited for extracting information from measured data than methods that represent the variables at a single scale. This paper presents an ove rview of multiscale data analysis and empirical modeling methods based on w avelet analysis. These methods exploit the ability of wavelets to extract e vents at different scales, compress deterministic features in a small numbe r of relatively large coefficients, and approximately decorrelate a variety of stochastic processes. Multiscale data analysis methods for off-line and on-line removal of Gaussian stationary noise eliminate coefficients smalle r than a threshold. These methods are extended to removing non-Gaussian err ors by combining them with multiscale median filtering. Multiscale empirica l modeling methods simultaneously select the most relevant features while d etermining the model parameters, and may provide more accurate and physical ly interpretable models. Copyright (C) 1999 John Wiley & Sons, Ltd.