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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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Journal ArticleDOI
Color image encryption based on interference and virtual optics
TL;DR: Two approaches to encrypt color images based on interference and virtual optics are proposed and a concept based on virtual optics is further applied to enhance the security level.
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Digital in-line holography in thick optical systems: application to visualization in pipes
TL;DR: The proposed model has the ability to deal with various pipe shapes and thicknesses and compensates for the lack of versatility of classical digital in-line holography models.
Concentrated signal extraction using consecutive mean excision algorithms
TL;DR: A focus is on concentrated signal extraction using blind, iterative and low-complex consecutive mean excision (CME) -based algorithms that can be applied to both IS and detection, and new CME-based methods are proposed and evaluated.
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Uncertainty principles associated with quaternionic linear canonical transforms
TL;DR: In this paper, the authors generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic LCT (QLCT), and establish an uncertainty principle for the two-sided QLCT.
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Sampling theorems for signals periodic in the linear canonical transform domain
Li Xiao,Wenchang Sun +1 more
TL;DR: In this article, Margolis and Eldar derived a similar reconstruction formula for a large class of signals, whose linear canonical transforms are band-limited periodic functions, and generalized this result in a broader sense.