The weighted gyrator transform with its properties and applications

Gyrator transform is a useful tool for information processing that produces twisted rotations in position-spatial frequency planes of phase space and belongs to the class of linear canonical integral transformations. In this paper, we presented a new twisting type of transform by using a different fractionalization process. Unlike the gyrator transform, the newly defined transform cannot be decomposed into a product of two one-dimensional transforms. Therefore it has a better capability of information-tangling than gyrator transform. The transform can be implemented by a photoelectric hybrid setup. Based on the new transform and a chaotic map, we proposed a watermarking scheme of which the viability and performance are demonstrated by means of numerical simulations.