Fast Block Jacket Transform Based on Pauli Matrices

Jacket matrices motivated by the center weight Hadamard matrices have play some important roles in signal processing and communication. In this paper we proposed a notation called block jacket matrices which substitute elements of matrices into matrices or even block matrices. Employing the well-known Pauli matrices which are very important in many subjects, several kind of block jacket matrices are constructed. Especially, construction and properties of the block jacket matrices with size 2ⁿ and 3ⁿ are investigated. Then a general approach for any size block jacket matrices is proposed. With novel properties of the block jacket matrices, a fast block inverse jacket transform is suggested.