Jaenisch, Holger M., Handley, James W., and Albritton, Nathaniel G. (2009) Converting data into functions for continuous wavelet analysis. In: Proceedings of SPIE 2009 - The International Society for Optical Engineering (7343) From: SPIE 2009 - The International Society for Optical Engineering, 13 -17 April 2009, Orlando, Florida, USA.

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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.

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