对几个小波基本概念的理解

讨论实际应用中经常涉及但容易产生误解的小波基本概念,以期提高电力系统小波应用研究水平。这些小波基本概念是:容许性条件;二进离散与二进小波;连续小波的离散条件;小波基;A=B=1的紧框架与正交小波;小波滤波器长度与时域分辨率;小波的滤波特性与不同尺度小波的频带交叠;线性相位小波与信号完全重构;双正交小波的小波包及小波包分解与1/2频程分解;整数倍伸缩小波变换与分数倍伸缩小波变换;小波的正则度与消失矩;Motlet函数与Morlet小波;小波变换模极大值(定义、与突变点位置的关系、与Lipschitz指数的关系、对小波的要求);时域、频域同时紧支小波;(时域)紧支正交线性相位小波;表征小波特性的基本指标与有价值的新小波。

SOME BASIC CONCEPTS OF WAVELETS

Some basic but sometimes confused concepts on wavelets are discussed. These include admissibility condition, dyadic dilation and dyadic wavelets, sampling restriction on continuous wavelets, wavelet bases, wavelet frames with A = B = l and orthogonal wavelets, filter length and time resolution of wavelets, overlapping octave bands of wavelets, linear phase wavelets and perfect reconstruction, biorthogonal wavelet packets, wavelet packet analysis and 1/2 octave splitting, integer and non-integer dilation MRA, regularity and vanishing moment of wavelets, Morlet function and Morlet wavelet, modulus maximum value of wavelet transform, compactly supported wavelets in time-and-frequency domains, compactly supported orthogonal wavelets with linear phase, basic characteristics of wavelets and new wavelets.