一类新的复解析子波构造及其性质研究

 基于Bubble子波和超高斯谱子波的构造方法,本文系统地提出一类新的复解析子波,该类子波在频域和时域均有简明的解析表达式.文中首先讨论用于实信号(线性)解析分析的母波构造条件,引出一类新的母波函数,然后从频域和时域两方面研究这类新母波的基本特性.根据本文的构造方法,调整少量几个控制参变量,就可得到许许多多具有不同性能的解析子波,并且某些经典的子波可归纳于新的子波函数类中,或者用新子波类中的某一特定元素逼近.

On a Novel Class of Complex Analytic Wavelet

By constructing bubble wavelet and supper Gaussian spectrum wavelet,a novel class of wavelet,along with its simple explicit expressions in frequency domain and time domain is presented systematically in this paper.Firstly,the conditions of constructing wavelet used for linear complex analysis of real signal are discussed,and then a new class of wavelet with generalizing linear phase (or Y wavelet) is introduced.Secondly,the basic performances and features of these new wavelets are studied in both frequency domain and time domain.Based on the proposed wavelet,a number of complex analytic wavelet with different performance and features are obtained by changing a few controlling parametric variables.Some of the existing wavelets is included in this new class of wavelets,or approximated by a specific member of this new class of wavelets.