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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
Initial and Final Value Theorem on Fractional Hankel Transform
TL;DR: In this paper, the authors established the initial and final value theorem for the generalized fractional Hankel transform, which is a generalization of the Hankel Transform and has many applications.
Journal ArticleDOI
Some families of series identities and associated fractional differintegral formulas
TL;DR: In this article, a number of closely-related fractional differintegral formulas associated with power, composite and rational functions were investigated individually and the main object of the present sequel to these earlier works is to consider some general results and their applications and consequences leading to many of the aforementioned fractions.
Proceedings ArticleDOI
A robust and efficient SAR ATR algorithm using a hybrid model of fractional fourier transform and pulse coupled neural network
Santu Sardar,Amit Mishra +1 more
TL;DR: A hybrid framework consisting of Fractional Fourier Transform and Pulse coupled Neural network (PCNN) is proposed in this paper for highly accurate and orientation, position & scale invariant synthetic aperture radar (SAR) automatic target recognition (ATR).
Journal ArticleDOI
Improved chirp scaling algorithm based on new integral kernel
TL;DR: A new integral kernel is proposed for the chirp scaling algorithm (CSA) to reduce the mismatched error of the shift-invariant range matched filter using a quadratic term of the temporal variable beside the linear term in the integral kernel of range transformation.
Three-Dimensional Image Watermarking Using Fractional Fourier Transform
TL;DR: Results of computer simulation have been presented in support of the proposed watermarking scheme and the watermark is recovered by applying the corresponding correct fractional orders and random phase masks.