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.

As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.

The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but es-sentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been com-prehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.

Linear canonical transform (LCT) is an integral transform with four parameters a, b, c, d and has been shown to be a powerful tool for optics, radar system analysis, filter design, phase retrieval, pattern recognition, and many other applications. Many well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper, new sampling formulae for reconstructing signals that are band-limited or time-limited in the linear canonical transform sense have been proposed. Firstly, the sampling theorem representation of band-limited signals associated with linear canonical transform from the samples taken at Nyquist rate is derived in a simple way. Then, based on the relationship between the Fourier transform and the linear canonical transform, the other two new sampling formulae using samples taken at half the Nyquist rate from the signal and its first derivative or its generalized Hilbert transform are obtained. The well-known sampling theorems in Fourier domain or fractional Fourier domain are shown to be special cases of the achieved results. The experimental results are also proposed to verify the accuracy of the obtained results. Finally, discussions about these new results and future works related to the linear canonical transform are proposed.

This paper describes an improved self-organizing CPN-based (Counter-Propagation Network) fuzzy system. Two self-organizing algorithms IUSOCPN and ISSOCPN, being unsupervised and supervised respectively, are introduced. The idea is to construct the neural-fuzzy system with a two-phase hybrid learning algorithm, which utilizes a CPN-based nearest-neighbor clustering scheme for both structure learning and initial parameters setting, and a gradient descent method with adaptive learning rate for 8ne tuning the parameters. The obtained network can be used in the same way as a CPN to model and control dynamic systems, while it has a faster learning speed than the original back-propagation algorithm. The comparative results on the examples suggest that the method is fairly e:cient in terms of simple structure, fast learning speed, and relatively high modeling accuracy.

For optimal polarization reception in the presence of interference and noise, a new signal-to-interference-and-noise-ratio (SINR) equation is derived from two triangles in polarization sphere based on the polarization ellipse parameters. The local optimal solutions of SINR on the great circle tracks and the small circle tracks are obtained. Some analytic solutions in special polarization schemes are presented. Several optimal strategies are proposed. An optimal polarization scheme called Three Steps’ Searching and Comparing (TSSC) is suggested. The comparison among these optimal schemes is given. Simulation results show that TSSC scheme closely approaches the global optimum quickly and efficiently.