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 Zopf
⁴
, 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.