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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
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Proceedings ArticleDOI
The direct batch generation of Hermite-Gaussian-like eigenvectors of the DFT matrix using the notion of matrix pseudoinverse
TL;DR: The contributed technique is termed the Direct Batch Evaluation by constrained Optimization Algorithm using the notion of matrix Pseudoinverse (DBEOAP), and the simulation results show that the DBEOAP results in smaller values of the norms of the approximation error vectors than those obtained when applying theDBEOA.
Proceedings ArticleDOI
Fractional Order Tchebichef Moment and its Invariants
TL;DR: A generalized order of Tchebichef polynomial and its translation, scale and rotation invariants are proposed and derived respectively and the results demonstrate the robustness of proposed invariants.
Posted Content
Violation of Bell's Inequality with Continuous Variables and Fractional Fourier Transforms
Stephen P. Walborn,Daniel S. Tasca,Marcelo P. Almeida,P. Pellat-Finet,Carlos H. Monken,P. H. Souto Ribeiro +5 more
TL;DR: This paper has been withdrawn due to a crucial theoretical error as mentioned in this paper, and the paper can be found in the archives of the University of Edinburgh, UK. http://www.ucla.edu.uk/
Journal ArticleDOI
Optimal representation and processing of optical signals in quadratic-phase systems
Sercan O. Arik,Haldun M. Ozaktas +1 more
TL;DR: In this paper, a non-redundant representation of the optical fields with the minimum number of samples is obtained by appropriate choice of sample points on these surfaces, and the non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs.
Proceedings ArticleDOI
Radon-Wigner transform processing for optical communication signals
TL;DR: In this paper, the temporal Radon-Wigner transform (RWT) is employed as a processing tool for pulses with FWHM of ps-tens of ps, commonly found in fiber optic transmission systems.