Duality properties for the variants of the Discrete W Transform (DWT)

Abstract

This paper gives the derivations of new duality properties for the four variants of the DWT. DWT and its variants are finite durational discrete transforms that are used in a host of applications in the fields of Digital Signal Processing, Digital Image Processing, Communication Systems, among a host of others. The Duality properties can be applied for the computation of the temporal signal from its frequency-domain counterpart or contra if and only if existing pair of DWT, including their counterparts, are known. The utility of the Duality properties lie in the abatement of computational complexity and disbursement intrinsically.