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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
Fractional discrete q-Fourier transforms
TL;DR: In this paper, the authors examined a family of q-extensions of the Mehta basis of the discrete Fourier transform (DFT) matrix and suggested that the account of fractional Fourier transformations applied on signals may be biased because the support of the function lies in the central part of the domain.
Efficient way of image encryption using generalized weighted fractional fourier transform with double random phase encoding
TL;DR: The GWFRFT is developed which is based on the properties of conventional FRFT and the random phase encoding technique in FRFT domain is discussed and random phase encode technique in GWFR FT domain is studied.
Journal ArticleDOI
ABORT-like detector to combat active deceptive jamming in a network of LFM radars
TL;DR: In this article, an adaptive detector exploiting generalized likelihood ratio test (GRLT) criterion is applied to detect the presence of deceptive jamming in fractional Fourier transform (FrFT) domain.
Proceedings ArticleDOI
A novel wavelet transform algorithm for image encryption
Hone-Ene Hwang,Pin Han +1 more
TL;DR: A high efficiency digital security system based on the discrete chirp parent wavelet transform (DCPWT) is introduced that is outstanding on two aspects: no iterations are needed and the image is recovered exactly (no information is lost).
DatasetDOI
N-dimensional Heisenberg’s uncertainty principle for fractional Fourier transform
TL;DR: In this article, a sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from NDF to two NDF transform domains, and conditions that reach the equality relation of the uncertainty inequalities are deduced.