Specific intelligent Traits of a kind of Quarternary Wavelet Packs with an Integer-valued Expansive Dilation Matrix

摘要

In this work, the notion of orthogonal nonseparable quarternary wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is introduced. The definition for orthogonal nonseparable quarternary wavelet packs is presented by iteration method. The orthogonality characters of quarternary wavelet packs are discussed. Three orthogonality formulas concerning these wavelet packets are established. Moreover, it is shown how to obtain new orthogonal bases of space L~2(R~4) from these wavelet packets.