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Proceedings Paper

Converting data into functions for continuous wavelet analysis
Author(s): Holger M. Jaenisch; James W. Handley; Nathaniel Albritton
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Paper Abstract

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.

Paper Details

Date Published: 19 March 2009
PDF: 12 pages
Proc. SPIE 7343, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering VII, 734309 (19 March 2009); doi: 10.1117/12.817870
Show Author Affiliations
Holger M. Jaenisch, Licht Strahl Engineering Inc. (United States)
James Cook Univ. (Australia)
Amtec Corp. (United States)
James W. Handley, Licht Strahl Engineering Inc. (United States)
Amtec Corp. (United States)
Nathaniel Albritton, Amtec Corp. (United States)


Published in SPIE Proceedings Vol. 7343:
Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering VII
Harold H. Szu; F. Jack Agee, Editor(s)

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