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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Journal ArticleDOI
Azimuth fractional transformation of the fractional chirp scaling algorithm (FrCSA)
A.S. Amein,John J. Soraghan +1 more
TL;DR: A closed-form expression for the azimuth FrFT of the FrCSA is mathematically derived and analyzed from the high-resolution synthetic aperture radar imaging point of view.
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Fractional Fourier transforms on Lp and applications
TL;DR: In this article, the L p (R ) theory of the fractional Fourier transform (FRFT) for 1 ≤ p 2 was studied and the regularity of fractional convolution and pointwise convergence of FRFT means were obtained.
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Uncertainty principle for linear canonical transform using matrix decomposition of absolute spread matrix
TL;DR: A new perspective is given on a key relation associated with spreads in time, frequency, time-frequency and linear canonical transform (LCT) domains, from which a new LCT uncertainty principle for complex signals using the ASM's rotation orthogonal decomposition is derived.
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QRS complex detection using fractional Stockwell transform and fractional Stockwell Shannon energy
Aditi Bajaj,Sanjay Kumar +1 more
TL;DR: A novel technique by amalgamating fractional Fourier transform and Stockwelltransform i.e., fractional Stockwell transform (FrST) for improving the accuracy and simultaneously suppressing artifacts affecting the ECG is introduced.
Journal ArticleDOI
Generalized Prolate Spheroidal Wave Functions Associated With Linear Canonical Transform
TL;DR: The sampling theorem associated with linear canonical transform is used to investigate an operator whose effect on a signal is to produce its first time-limited then (b, b, c, d)-band-limited version.