Characterization Of The Image Space In The Limited Spectrum Wavelets Transform

In the 1980 s,wavelet analysis has become a new branch of mathematics in the field of mathematics,It is also a major breakthrough in the application of mathematical tools in engineering field after Fourier analysis.At present,it has been active in pure mathematics,applied mathematics and signal processing and other fields.According to the wavelet analysis in signal processing,it not only can do local exchange at the same time in time and frequency,but also can extract useful information from the signal effectively.Therefore,wavelet analysis theory can solve many difficult problems better than Fourier transform.Wavelet analysis is based on continuous wavelet transform,while reproducing kernel space is the basis of continuous wavelet transform.In this paper,we study the specific spectral finite wavelet and its wavelet transform image space as reproducing kernel Hilbert space,Specific contents are as follows:In order to describe the nature of image space of the wavelet transform and a limited spectrum and decay faster wavelet,this paper uses Shannon scaling function to construct a wavelet function,take advantage of wavelet analysis theory to give the nature of image space of the wavelet transform and the wavelet transform.Fixing the scale factor,we get this wavelet transform as the space of two specific expressions of reproducing kernel function,take advantage of the reproducing kernel space theory to describe the wavelet transform of image space.In addition,we study the dyadic wavelet of finite frequency spectrum,in the time domain with symmetry,decay,smoothness,in the frequency domain with compact support,locality,etc.Firstly,this paper gives the isometric identities and estimation of the dyadic wavelet transform,then the analytic expression of the reproducing kernel function of the dyadic wavelet transform image space.It provides the basis for the study of the general wavelet transform's image space.