The Jacket Transform, Jackets, Matrix Structure And Application

Jacket matrix basic idea was motivated by the cloths of Jacket. As our two sided Jacket is inside and outside compatible, at least two positions of a Jacket matrix are replaced by their inverse; these elements are changed in their position and are moved, for example, from inside of the middle circle to outside or from to inside without loss of sign。The Walsh-Hadamard transform (WHT) and discrete Fourier transform (DFT) are widely used in signal processing. In particular, these transforms are used in image coding and processing and error-control coding.Variations of these two transforms, called the center weighted Hadamard transform (CWHT) and the complex reverse jacket transform (CRJT) have been reported. The jacket transform is so named because it brings to mind a reversible jacket. Just as the jacket is easily reversed (turned inside out), so too the jacket matrix is easily inverted. The CWHT and CRJT can be seen as generalizations of the WHT.This paper first has simply introduced hadamard matrices and discrete fourier transform, which are widely used in signal processing, in particular, these transform are used in image coding and processing and error-control coding. Second, we will talk about the definition of jacket matrix and its advantage and research progress. We use Kronecker product to construct from lower-order reverse jacket matrix and hadamard matrix to larger-order. Meanwhile, we will get the general formula of construct reverse jacket matrix. We present some example of jacket matrix and reverse jacket matrix in code division multiple access, coding and signal processing.finally, to the paper summarized and prospect.