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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An Extrapolation Algorithm for -Bandlimited Signals
TL;DR: In this article, an iterative -bandlimited signal extrapolation algorithm is proposed by using the interesting properties of generalized prolate spheroidal wave functions, and the convergence of the proposed algorithm is proved.
Journal ArticleDOI
Target Image Enhancement in Radar Imaging Using Fractional Fourier Transform
TL;DR: A new Range-Doppler Algorithm based on Fractional Fourier Transform (RDA-FrFT) to obtain High-Resolution (HR) images for targets in radar imaging and takes its advantage of the property of the FrFT to resolve chirp signals with high precision.
Journal ArticleDOI
Fractional free space, fractional lenses, and fractional imaging systems.
Uygar Sümbül,Haldun M. Ozaktas +1 more
TL;DR: Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform, revealing precisely how they are interpolations of their conventional counterparts.
Dissertation
Sparsity and convex programming in time-frequency processing
TL;DR: The proposed methods aim to obtain high resolution and cross-term free TF representations using sparsity and lifted projections using a new kernel estimation method based on a single projection onto the epigraph set of l1 ball in TF domain.
Journal ArticleDOI
Signal-tuned gabor functions as models for stimulus-dependent cortical receptive fields
TL;DR: By modeling the receptive fields of simple and complex cells as signal-tuned Gabor functions and expressing their responses as STGTs, this work is able to replicate the properties of these cells when tested with standard grating and slit inputs, at the same time emulating their stimulus-dependent character as revealed by recent neurophysiological studies.