An analytical expression of an Airy-Gauss beam passing through a fractional Fourier transform (FRFT) system is derived. The normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are demonstrated in FRFT plane, respectively. The influence of the fractional order p on the normalized intensity d...

The original definition of the derivatives of a function makes sense only for integral orders, i.e. we can speak of the first or second derivative and so on. However, it is possible to extend the definition of the derivative to noninteger orders by using an elementary property of Fourier transforms. Bracewell shows how fractional derivatives can be used to characterize the discontinuities of ce...

We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yetelegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the co...

A method of optimal beamforming for Rayleigh-faded time-frequency selective channels using fractional Fourier transform (FRFT) is considered in this paper. The conventional minimum mean squared error (MMSE) beamforming in the frequency domain or spatial domain becomes a special case of optimal beamforming with FRFT. The method is especially useful in moving source problems, where Doppler effect...

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

Due to the fast evolution of digital data exchange, security of information becomes important. For industrial process images are used widely, therefore it is necessary to protect the confidential information. In the proposed work for encryption of image by the use of Fractional Fourier Transform(FRFT).This method enhances the security of data in comparison to DFT. In the proposed work we will b...

The uncertainty principles of the 1-D fractional Fourier transform and the 1-D linear canonical transform have been derived. We extend the previous works and discuss the uncertainty principle for the two-dimensional affine generalized Fourier transform (2-D AGFFT). We find that derived uncertainty principle of the 2-D AGFFT can also be used for determining the uncertainty principles of many 2-D...

This paper deals with the performance of the use of fractional Fourier transform (FRFT) instead of conventional Fourier transform (FFT) in either symbol timing offset (STO) and carrier frequency offset (CFO) estimation. Orthogonal frequency division multiplexing is widely used in many systems due to advantages of theses technique compared with mono-carrier systems. In spite of his advantages, O...

As the useful time-frequency tool, the Fractional Fourier Transform (FRFT) and the Short Time Fourier Transform (STFT) have a great development of signal recognition. And the Reduced Fractional Fourier Transform (RFRFT) was recently proposed and has been used in the recognition and estimation of chirp signals. A new method based on STFT and RFRFT is presented for radar signals modulation recogn...