Converting Data into Functions for Continuous Wavelet Analysis

机译：将数据转换为连续小波分析的函数

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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.

机译：我们展示了如何将连续小波变换（CWT）应用于离散数据。这是通过从n阶可积分和微分数据中导出分析函数来完成的。我们还将展示如何使这些数据模型得到紧凑的支持。此外，我们展示了如何为数据采样过程确定停止标准以启动小波变换。我们还建议如何利用数据间隔从采样数据中获取分形小波母函数。我们将其与经典技术进行比较，并注意到其性能得到了提高，最后展示了如何通过仅使用余弦函数转换为单边双谱形式来最小化分析数据模型中的项数。通过这种双谱形式，我们能够预测并回播原始数据和派生的自适应基函数。

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来源
《ICA;Conference on independent component analyses, wavelets, neural networks, biosystems, and nanoengineering VII; 20090413-17;20090413-17; Orlando, FL(US);Orlando, FL(US)》|2009年|P.734309.1-734309.12|共12页
会议地点 Orlando FL(US);Orlando FL(US)
作者
Holger M. Jaenisch; James W. Handley; Nathaniel G. Albritton;
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LSEI Consultants, Toney, AL 35773 James Cook University, Townsville QLD 4811, Australia Amtec Corporation, 500 Wynn Dr., Suite 314, Huntsville, AL 35816;

LSEI Consultants, Toney, AL 35773 Amtec Corporation, 500 Wynn Dr., Suite 314, Huntsville, AL 35816;

Am;

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原文格式 PDF
正文语种 eng
中图分类信息处理（信息加工）;
关键词
data modeling; wavelet analysis; unifluxion; bi-spectral modeling; adaptive basis function; bi-cos; predictive wavelet; forecast; automatic differential equation; fractal wavelet; self-remapped function;

机译：数据建模;小波分析;单通量;双谱建模;自适应基函数; bi-cos;预测小波;预测;自动微分方程;分形小波;自重映射函数;

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Converting Data into Functions for Continuous Wavelet Analysis

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