Decay properties of the discrete wavelet transform in n dimensions with independent dilation parameters

Journal of Inequalities and Applications

Jaime Navarro¹  Oscar Herrera² 

[1] Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana;Departamento de Sistemas, Universidad Autónoma Metropolitana;

关键词: discrete wavelet transform;    tight frames;    reconstruction formula;   

DOI  :  10.1186/s13660-016-0961-z

来源: DOAJ

【 摘 要 】

Abstract The purpose of this paper is to study the decay properties of the discrete wavelet transform with n independent dilation parameters for functions f in L 2 ( R n ) $L^{2}({ {\mathbb {R}}}^{n})$ and a relationship with its continuity. The method we used to study the discrete wavelet transform of f with respect to a radially symmetric admissible function was through the fact of considering two parameters in Z n ${ {\mathbb {Z}}}^{n}$ . We conclude that the continuity of f at x = 0 $x=0$ is determined by the existence of the limit of the discrete wavelet transform when each one of the independent dilation parameters tends to zero.

【 授权许可】

Unknown