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
A sampling theorem for the fractional Fourier transform without band-limiting constraints
TL;DR: A sampling theorem without band-limiting constraints for the fractional Fourier transform in the function spaces is established, which can provide a suitable and realistic model of sampling and reconstruction for real applications.
Journal ArticleDOI
Closed-form designs of digital fractional order Butterworth filters using discrete transforms
Chien-Cheng Tseng,Su-Ling Lee +1 more
TL;DR: Close-form designs of digital fractional order Butterworth (FOB) filters using discrete transform methods are presented and application examples in the digital image sharpening are studied to demonstrate the effectiveness of proposed FOB filter design approaches.
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A discrete fractional angular transform
TL;DR: A new discrete fractional transform defined by two parameters (angle and fractional order) is presented that can be applied in one and two dimensional signal processing and has very important practical applications in signal and image processing.
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Transformation of double-half inverse Gaussian hollow beams into superposition of finite Airy beams using an optical Airy transform
TL;DR: In this paper, the authors investigated theoretically the transformation of a double-half inverse Gaussian hollow (DHIGH) beam into a superposition of finite Airy beams by using an optical Airy transform system.
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Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform.
TL;DR: It is shown that by judiciously choosing sample points on these curved reference surfaces, it is possible to represent the diffracted signals in a nonredundant manner and provide a simple and robust basis for accurate and efficient computation.