基于尺度能量参数的子波变换及其应用

提出基于尺度能量参数的子波变换方法。首先给出了尺度能量参数的概念，讨论基于这一参数的子波变换的时频特性，然后推导基于尺度能量参数的子波变换的逆变换，给出并证明其容许性条件成立的充分条件。文中给出基于尺度能量参数的子波变换中尺度与波长的关系，并且分析了一组黄河上游年径流量数据。研究结果表明，基于尺度能量参数的子波变换能够放大、突出不同尺度下的信号特征。

Wavelet Transform Based on Scale-Energy Parameter and Its Application

A method for wavelet transform based on scale-energy parameter is proposed. Firstly, a brief concept about the traditional wavelet transform is given, and the scale-energy parameter is proposed. Then the wavelet transform based on the scale-energy parameter is constructed, the properties of time-frequency space involved in the wavelet transform are investigated. The inverse wavelet transform based on the scale-energy parameter is deduced, and the sufficient condition which makes the admissibility condition be satisfied is presented and proved. The relationship between the scale and the wavelength is given, and a natural annal flow time series in the upper reach of the Yellow River is analyzed. Experimental results show that using the wavelet transform based on scale-energy parameter, the localized signal features can be magnified at different scales.