A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption.

In this letter, we generalize the fractional Hilbert transform of a real signal to get an analytic version which contains no negative spectrum while maintaining the essential information of the real signal. We also present a secure single-sideband (SSB) modulation system in which the angle of the fractional Fourier transform and the phase of the fractional Hilbert transform are used as double keys for demodulation.

The focus of this research is to provide a fast and precise method for joint time delay and Doppler shift estimation. The main procedure is divided into two stages. In the first stage, the preweighted Zoom fast Fourier transform and quadratic surface fitting methods are used for fast computing the ambiguity function and the for coarse estimation, respectively. In the second stage, the values near the coarse estimates are calculated and quadratic surface fitting method is used again for fine estimation. The two-stage method reduces the computational load without losing the precision. Simulation and experimental results are used to demonstrate the effectiveness of the proposed method.

A novel image encryption method is proposed by utilizing random phase encoding in the fractional Fourier domain to encrypt two images into one encrypted image with stationary white distribution.By applying the correct keys which consist of the fractional orders,the random phase masks and the pixel scrambling operator,the two primary images can be recovered without cross-talk.The decryption process is robust against the loss of data.The phase-based image with a larger key space is more sensitive to keys and disturbances than the amplitude-based image.The pixel scrambling operation improves the quality of the decrypted image when noise perturbation occurs.The novel approach is verified by simulations.

The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital frequency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sampling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.