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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
Analysis of Chirp as windowing function through fractional Fourier transform
TL;DR: In this paper, a new mathematical model for obtaining the fractional Fourier transform (FrFT) of Chirp function is presented, which is a parameterised transform having an adjustable transform parameter which makes it more flexible and superior over ordinary FT.
Journal ArticleDOI
The Properties and Fast Algorithm of Quaternion Linear Canonical Transform
Ye Zhang,Guanlei Xu +1 more
TL;DR: In this paper, the quaternion linear canonical transform (QLCT) is defined and its physical interpretation is given as classical convolution, correlation and product theorem, and the fast algorithm of QLCT is obtained, whose calculation complexity for different signals is similar to FFT.
Proceedings ArticleDOI
Generalized sampling theorem for bandpass signals associated with fractional Fourier transform
TL;DR: A new generalized sampling theorem associated with the FRFT from the fractional bandpass signal viewpoint is proposed which is constructed by the ordinary convolution in the time domain and can overcome the effect of spectral leakage.
Proceedings ArticleDOI
A fast two-dimension Discrete Fractional Fourier Transform algorithm and its application on digital watermarking
TL;DR: The feasibility of the two-dimension algorithm is proved by its successful application in the domain of digital watermarking and its sensitivity to attacks in both the spatial domain and the frequency domain indicates that the algorithm can be applied to make fragile watermarkings.
Journal ArticleDOI
Suppression of Cross-Channel Interference Based on the Fractional Fourier Transform in Polarimetric Radar
TL;DR: A new cross-channel interference suppression method based on the fractional Fourier transform (FRFT) is proposed to eliminate the effect due to cross-Channel interference when a full-polarimetric radar adopts the opposite-slope linear frequency modulation transmit signals and de-ramping processing in the simultaneous measurement mode.