Wavelet analyses and applications

Abstract

It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each frequency as a function of time. Next, the theory is specialized to discrete values of time and frequency, and the resulting discrete wavelet transform is shown to be useful for data compression. This paper is addressed to a broad community, from undergraduate to graduate students to general physicists and to specialists in other fields than wavelets.

Multiscale error analysis, correction, and predictive uncertainty estimation in a flood forecasting system

“…In recent years the development of wavelet theory has spawned applications in signal processing and time series analysis, and fast algorithms for integral transforms and image and function representation methods. A summary of the latest developments in the area of wavelet analysis and its applications can be found for example in the work by Bordeianu et al [2009] and Qian et al [2007]. Wavelet transformation provides a very useful and efficient decomposition tool for time series in terms of both time and frequency [see Mallat , 1989].…”

Effect of Multiple Factors on Identification and Diagnosis of Skidding Damage in Rolling Bearings under Time-Varying Slip Conditions

“…Although Fourier transform can transform the signal from the time-domain analysis to the frequency-domain analysis, the corresponding time-domain information is lost during the transformation, and hence it cannot provide comprehensive and effective information for fault diagnosis and analysis. Wavelet analysis is an extension of Fourier analysis [23,24]. DWT is usually used to analyze nonlinear and non-stationary time-frequency signals.…”