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

Abstract

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.

Keywords

• discrete wavelet transform
• tight frames
• reconstruction formula