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
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Proceedings ArticleDOI
Performance evaluation of transform selective interference suppression
TL;DR: This paper investigates the transform selective interference suppression algorithm (TSISA), which is an adaptive method for suppressing several types of interferences, based on several parallel transforms, in which the most suitable transform domain is chosen.
Journal ArticleDOI
Linear Summation of Fractional-Order Matrices
Ran Tao,Feng Zhang,Yue Wang +2 more
TL;DR: It is found that for any diagonalizable periodic matrices, linear summation of fractional-order forms with special orders is related to the size and the period of the fractional -order matrix.
Proceedings ArticleDOI
Discrete windowed linear canonical transform
TL;DR: In this article, a necessary and sufficient condition for discrete windowed linear canonical transform being a Riesz basis is derived. But this condition is not applicable to the case where the canonical transform is a frame.
Journal ArticleDOI
Hamiltonian orbit structure of the set of paraxial optical systems
TL;DR: This paper resolves the degeneracies of the eigenvalue classification in the paraxial regime of three-dimensional optics by using the orbit analysis of the algebra sp(4, R) of 4 x 4 real Hamiltonian matrices to find four orbit regions (strata) and six degenerate orbits at their common point.