论文部分内容阅读
将传统意义下的整数阶微分运算拓展到非整数阶微分情形 ,直接仿照整数阶微分在时域的极限定义形式是很困难的 .本文从分析微分运算的频域形式着手 ,将微分算子分解成幅度算子和相位算子 ,并将其与子波变换特征进行比照研究 ,从而解决了非整数阶微分的拓展问题 ,同时也得到了微分运算与子波变换的内在联系 ,为非整数阶微分计算提供了一种逼近方式 .文中提出了幅度算子、广义Hilbert变换等新概念并重点探讨了基于非整数阶微分运算的子波构造及其局域化特征等问题
It is very difficult to extend the integral differential operation in the traditional sense to a non-integer order differential case and directly follow the definition form of the limit of integer order differential in the time domain.This paper starts from analyzing the frequency domain form of differential operation, decomposes the differential operator Scale operator and phase operator and compare them with wavelet transform characteristics to solve the expansion problem of non-integer differential and obtain the inner relationship between differential operation and wavelet transform. Differential computation provides an approximation approach. In this paper, new concepts such as amplitude operator and generalized Hilbert transform are proposed and the wavelet structure and its localization characteristics based on non-integral differential operation are discussed emphatically