Image representation of a signal for a fractional Fourier transform watermarking scheme

This work introduces a signal watermarking scheme employing the fractional Fourier transform in the time-frequency domain. The proposed scheme employs an image representation of a signal, the so-called time-frequency representation, in order to embed the watermark, whereas the detector is applied on the fractional time-frequency distribution. Thus, it benefits from the two additional degrees of freedom, associated with the two angles of the 2D fractional Fourier transform, which allow hiding more watermarks than the ones allowed in 1D time or frequency domains. The proposed scheme is experimentally tested on mono-component and multi-component frequency modulated signals. It is shown that watermarking by means of 2D fractional Fourier transform achieves almost perfect detectability for noiseless signals and results in smaller distortions of the original 1D signal, than the ones induced by watermarking based on 1D fractional Fourier. In addition, the proposed watermarking scheme outperforms watermarking on 1D fractional Fourier domain in terms of robustness against noise.