The fractional fourier transform and its application to digital watermarking

Abstract

The Fractional Fourier transform (FrFT) is the generalization of the classical Fourier Transform. It depends on a parameter α = aπ/2 and can be interpreted as a rotation by an angle a in the time-frequency plane. This paper describes the implementation of a watermark embedding technique for images using the discrete fractional Fourier transform. The idea is that a 2D discrete fractional Fourier transform of the image is computed. In this transform domain, a watermark logo is used to modify the transform coefficients of the real and imaginary component. Then the inverse transform is applied to give the watermarked image. The detection is based on performing the same transform operation. The watermark is recognized if there is a strong correlation with the embedded watermark.