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
Sampling and series expansion for linear canonical transform
Deyun Wei,Yuan-Min Li +1 more
TL;DR: Two new sampling relations in the LCT domain are presented, where the signal in the time domain is reconstructed from the samples of its LCT directly, and the first theorem considers signals band-limited in some LCTdomain.
Journal ArticleDOI
Optical image encryption based on S-box transformation and fractional Hartley transform:
TL;DR: A novel technique for image encryption is established based on a two-dimensional generalization of a one-dimensional fractional Hartley transform that has been redefined in recent times in exploration of its inverse transform.
Book ChapterDOI
Linear Canonical Transform
Jian-Jiun Ding,Soo-Chang Pei +1 more
TL;DR: This chapter introduces the definitions, theories, physical meanings, and applications of the LCT and its generalized versions and states that it will play a very important role in signal processing in the future.
Journal ArticleDOI
A fractional Fourier transform analysis of the scattering of ultrasonic waves
TL;DR: The theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification.
Journal ArticleDOI
Stereo image coding via digital watermarking
TL;DR: A robust stereo-image coding algorithm using digital watermarking in fractional Fourier transform (FrFT) and singular value decomposition (SVD) to achieve stereo image security is presented.