Open AccessBook
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TLDR
The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.Abstract:
Preface. Acknowledgments. Introduction. Signals, Systems, and Transformations. Wigner Distributions and Linear Canonical Transforms. The Fractional Fourier Transform. Time-Order and Space-Order Representations. The Discrete Fractional Fourier Transform. Optical Signals and Systems. Phase-Space Optics. The Fractional Fourier Transform in Optics. Applications of the Fractional Fourier Transform to Filtering, Estimation, and Signal Recovery. Applications of the Fractional Fourier Transform to Matched Filtering, Detection, and Pattern Recognition. Bibliography on the Fractional Fourier Transform. Other Cited Works. Credits. Index.read more
Citations
More filters
Journal ArticleDOI
Signal reconstruction from the undersampled signal samples
TL;DR: In this article, a generalized low-pass sampling theorem for band-pass signals is presented and its special cases are discussed, and the sampling rate in this sampling theorem can be further reduced by a factor of two under some restricted conditions.
Journal ArticleDOI
Digital in-line holography assessment for general phase and opaque particle
Sébastien Coëtmellec,Wisuttida Wichitwong,Gérard Gréhan,Denis Lebrun,M. Brunel,Ajem Guido Janssen +5 more
TL;DR: In this article, the authors used the circle polynomials to describe a particle's transmission function in a digital holography setup and demonstrated that it is possible to estimate the digital in-line hologram produced by a spherical particle.
Journal ArticleDOI
First-order optical systems with unimodular eigenvalues.
TL;DR: It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodULAR system and the separable fractions of the separables are related by means of a similarity transformation.
Journal ArticleDOI
Image Encryption Based on Block-wise Fractional Fourier Transform with Wavelet Transform
TL;DR: A new method of image encryption using block-wise fractional Fourier transform (FRFT) with the subsequent use of discrete wavelet transform is proposed which gives high security as it is quite difficult to decrypt the image without knowing the proper keys.
Journal ArticleDOI
Uncertainty principles for the short-time linear canonical transform of complex signals
Wen-Biao Gao,Bing-Zhao Li +1 more
TL;DR: This paper generalizes some different uncertainty principles for the STLCT of complex signals in time and frequency domains to obtain the uncertainty principle for the two conditional standard deviations of the spectrogram associated with the STL CT.