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19 March 2009 Converting data into functions for continuous wavelet analysis
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We show how to apply the Continuous Wavelet Transform (CWT) to discrete data. This is done by deriving analytical functions from the data that are nth order integrable and differentiable. We also show how to make these Data Models compactly supported. Further, we show how to identify a stopping criteria for the data sampling process to initiate the wavelet transformation. We also suggest how the data interval can be exploited to obtain a fractal wavelet mother function from the sampled data. We compare this to classical techniques and note enhanced performance, and finally show how the number of terms in the analytical Data Model can be minimized by converting into a one-sided bi-spectral form using only cosine functions. From this bi-spectral form, we are able to forecast and backcast both the original data and the derived adaptive basis functions.
© (2009) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Holger M. Jaenisch, James W. Handley, and Nathaniel Albritton "Converting data into functions for continuous wavelet analysis", Proc. SPIE 7343, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering VII, 734309 (19 March 2009);

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