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
The fractional Fourier transform and quadratic field magnetic resonance imaging
TL;DR: It is shown how the fractional Fourier transform can be used to reconstruct Magnetic Resonance (MR) images acquired under the presence of quadratic field inhomogeneity and it is proved that the order of the FrFT is a measure of the distortion in the reconstructed signal.
Journal ArticleDOI
A robust security framework for 3D images
TL;DR: A novel security framework, viz., watermarking scheme, is presented to ensure 3D images/Anaglyphs security and the experimental results prove the robustness and imperceptibility of the proposed water marking scheme.
Posted Content
Applications of integral transforms composition method (ITCM) to wave-type singular differential equations and index shift transmutations
TL;DR: In this paper, the authors studied applications of integral transforms composition method (ITCM) for obtaining transmutations via integral transforms and derived a wide range of transmutation operators by this method.
Dissertation
Application of fractional calculus to engineering: a new computational approach
Raja Muhammad,Asif Zahoor +1 more
TL;DR: A new heuristic computational intelligence technique has been developed for the solution for fractional order systems in engineering that provides the solution on continuous time inputs with finite interval instead of predefine discrete grid of inputs.
Journal ArticleDOI
Uncertainty principle and orthogonal condition for the short-time linear canonical transform
TL;DR: This short paper develops the uncertainty principle in one STLCT domain and the orthogonal condition is proposed to guarantee the completeness of the STLCE coefficients.