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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
An Improved Product Theorem for Fractional Fourier Transform
TL;DR: In this paper, a better product theorem for fractional Fourier transform (FrFt) is proposed, which is more precise and relevant proposition than existing models, and it is shown to be more accurate and relevant than existing FrFt models.
Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application
TL;DR: This dissertation provides an implementable, general reconstruction framework for the issues related to reduction in the number of samples and estimation of nonuniform sample times and realizes time decoding modulation for an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants.
Proceedings ArticleDOI
The generalized fractional fourier transform
TL;DR: The integral forms of the gFrFTs are derived and they are closely related to some popular transforms, such as the Fourier transform (FT), the FrFT, and the complex linear canonical transform (CLCT).
Journal Article
Digital Hilbert optics methodology for complex shape objects and textures at dynamic scenes identification: structure design, modelling and verification
V. Vlasenko,A. Sudoł +1 more
Image produced by bessel-modulated gaussian beams propagating through a fractional fourier transform system with two hard-edged apertures
TL;DR: Based on the Fresnel diffraction theory, this article investigated a detailed study of image produced by a Besselmodulated Gaussian (QBG) beams propagating through a Fractional Fourier Transform system with two circular apertures.