In order to describe the nature of image space of the wavelet transform and a limited spectrum anddecay faster wavelet，this paper uses Shannon scaling function to construct a wavelet function，take advantage ofwavelet analysis theory to give the nature of image space of the wavelet transform and the wavelet transform. Fixingthe scale factor，we get this wavelet transform as the space of two specific expressions of reproducing kernelfunction，take advantage of the reproducing kernel space theory to describe the wavelet transform of image spaceand provide the theoretical basis for numerical calculation of the wavelet.