Generalizing the Jacket transform by sub orthogonality extension

The Jacket transform is a generalization of the Hadamard (Walsh) transform and useful in signal and image processing. In this paper, we will further generalize the Jacket transform defined in previous papers. We use the sub orthogonality property of the columns of the Walsh transform to define a more general form of the Jacket transform. For an N-point Jacket transform, there are N parameters that can be freely chosen. Therefore, it is possible to make the generalized Jacket transform have a certain form (such as the sinusoid-like form) while preserving the advantages of the original Walsh transform (reversibility, no multiplication, and the fast algorithm). As with the original Walsh and Jacket transforms, the proposed generalized Jacket transform will be helpful for CDMA and signal analysis.