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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 .
Based on the construction methods of Bubble wavelet and super-Gaussian spectrum wavelet, a new class of complex analytic wavelets is proposed systematically in this paper, which have simple analytic expressions in both frequency and time domains.In this paper, Signal (linear) analytic analysis of the mother wave structure conditions, leads to a new class of mother wave function, and then from the frequency domain and time domain two aspects of this new mother wave basic characteristics.According to the construction method of this article, adjust a small number of By controlling the parameters, many analytic wavelets with different properties are obtained, and some classical wavelets can be summarized in a new class of wavelet functions or approximated by a specific element in the new wavelet class.