Low-oscillation complex wavelets

In this paper we explore the use of two low-oscillation complex wavelets-Mexican hat and Morlet-as powerful feature detection tools for data analysis, These wavelets, which have been largely ignored to date in the scientific literature, allow for a decomposition which is more temporal than spectral in wavelet space. This is shown to be useful for the detection of small amplitude, short duration signal features which are masked by much larger fluctuations. Wavelet transform-based methods employing these wavelets (based on both wavelet ridges and modulus maxima) are developed and applied to sonic echo NDT signals used for the analysis of structural elements. A new mobility scalogram and associated reflectogram is defined for analysis of impulse response characteristics of structural elements and a novel signal compression technique is described in which the pertinent signal information is contained within a few modulus maxima coefficients. As an example of its usefulness, the signal compression method is employed as a pre-processor for a neural low classifier. The authors believe that low oscillation complex wavelets have wide applicability to other practical signal analysis problems. Their possible application to two such problems is discussed briefly - the interrogation of arrhythmic ECG signals and the detection and characterization of coherent structures in turbulent flow fields. (C) 2002 Elsevier Science Ltd. All rights reserved.