A new parametric transform
In this paper, a novel method for the parameterization of the Hadamard matrices is proposed. The resulting parametric Hadamard matrix of order N has N/2-1 independent parameters. It is a normalized matrix and its inverse can easily be obtained by taking the reciprocal of each of the N/2-1 independent parameters in the forward matrix and transposing the resulting matrix. The corresponding transform reduces to a new parametric integer transform when the independent parameters in the proposed matrix operator are all from the set {plusmn2m, plusmn 2n j, 2l (plusmn1plusmn j)}, where m, n and l are chosen positive or negative integers. Other interesting special cases of the proposed transform can also be obtained. In addition, the proposed parametric transform can be computed using an algorithm having a very simple structure. This transform can be used in many transform-based applications. For example, it can be employed in watermarking and encryption where its independent parameters can be used as an additional secret key.