The Generalized Weighted Fractional Fourier Transform and its Application to Image Encryption

In this paper, Shih´s weighted fractional Fourier transform is generalized to contain two 4D vector parameters IfrRfr, Rfr isin Zopf⁴, which is denoted by generalized weighted fractional Fourier transform (GWFRFT). The proposed GWFRFT is shown to possess all of the desired properties for Shih´s FRFT. In fact, the GWFRFT will reduce to Shih´s FRFT when both IfrRfr, Rfr are zero vectors. The eigenvalue relationships between GWFRFT and two original FRFT definitions are discussed. To give an example of application, we exploit its multiple-parameter feature and propose the double random phase encoding in the GWFRFT domain for digital image encryption. The proposed encoding scheme in the GWFRFT domain can enhances data security.