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 different localization in time and frequency. Consequently, data analysis and modeling methods that represent the measured variables at multiple scales are better suited for extracting information from measured data than methods that represent the variables at a single scale. This paper presents an overview of multiscale data analysis and empirical modeling methods based on wavelet analysis. These methods exploit the ability of wavelets to extract events at different scales, compress deterministic features in a small number 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 smaller than a threshold. These methods are extended to removing non-Gaussian errors by combining them with multiscale median filtering. Multiscale empirical modeling methods simultaneously select the most relevant features while determining the model parameters, and may provide more accurate and physically interpretable models. Copyright  1999 John Wiley & Sons, Ltd.