Differential Operator and the Construction of Wavelet
Xiao Hua Yuan · Dianzi xuebao · 2002
This paper investigates the topic of non integral order differentiation.Following directly the limit definition of the classical integral order differentiation in the time domain,it is difficult to expand the classical differential operation from the integral order case to the non integral order case.Based on the expression of differential operation in the frequency domain,and wedding it to the wavelet transform,the non integral order differential problem was solved in this paper.Meanwhile the inherent law between the non integral order differential operation and the wavelet transform was discovered,and an approximate approach for computing the non integral order differentiation was given.In this paper we introduce some new concepts,such as the magnitude operator and the generalized Hilbert transform etc,thereby study emphatically the construction and the localization characteristics of wavelet which is based on the non integral order differentiation of a low pass function.