Converting Data into Functions for Continuous Wavelet Analysis

摘要

We show how to apply the Continuous Wavelet Transform (CWT) to discrete data. This is done by deriving analyticalfunctions from the data that are n~thorder integrable and differentiable. We also show how to make these Data Modelscompactly supported. Further, we show how to identify a stopping criteria for the data sampling process to initiate thewavelet transformation. We also suggest how the data interval can be exploited to obtain a fractal wavelet motherfunction from the sampled data. We compare this to classical techniques and note enhanced performance, and finallyshow how the number of terms in the analytical Data Model can be minimized by converting into a one-sided bi-spectralform using only cosine functions. From this bi-spectral form, we are able to forecast and backcast both the original dataand the derived adaptive basis functions.