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Discrete fractional Hadamard transform (DFHaT) is a generalization of discrete Hadamard transform. It has been widely used in signal processing. Different from only having one order parameter, in this paper, a new generalized discrete fractional Hadamard transform (GDFHaT) is proposed, which has multi-order parameters. This kind of GDFHaT shares most properties with DFHaT. The GDFHaT becomes DFHaT when all of its order parameters are the same. Then we apply it to the image encryption. Results show this method performs well.

Generalized Discrete Fractional Hadamard Transformation and its Application on the Image Encryption