Approximate fractality of sea clutter fractional fourier transform spectrum

As a generalization of the classical Fourier Transform (FT), the Fractional Fourier Transform (FRFT) has many applications in several fields, such as optics and signal processing. In this paper, the scaling property of the FRFT spectrum is studied in depth and the approximate similarity between the FRFT spectra is presented. The analytical results show that the approximate similarity can be observed in some specific FRFT spectra of a time signal, which correspond to some specific transform orders (or rotating angles). In other words, the FRFT spectra of a time signal are approximate fractal at some specific transform orders. In the end, X-band and C-band real radar data is used for the verification of the conclusion.