Converting data into functions for continuous wavelet analysis

Holger M. Jaenisch; James W. Handley; Nathaniel Albritton

doi:10.1117/12.817870

19 March 2009 Converting data into functions for continuous wavelet analysis

Holger M. Jaenisch, James W. Handley, Nathaniel Albritton

Proceedings Volume 7343, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering VII; 734309 (2009) https://doi.org/10.1117/12.817870
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

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 n^th 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.

Citation Download Citation

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); https://doi.org/10.1117/12.817870

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