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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 dual tree complex wavelet transform and its application to biometric security during communication and transmission
TL;DR: In this paper, biometric is chosen as the primary application and hence a new technique is proposed for securing biometrics during communication and transmission over insecure channel, i.e. the fractional dual tree complex wavelet transform (FrDT-CWT).
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Maximum Amplitude Method for Estimating Compact Fractional Fourier Domain
Liying Zheng,Daming Shi +1 more
TL;DR: A maximum-amplitude-based coarse- to-fine algorithm is proposed with two novel ideas highlighted: adopting the maximum value of the fractional Fourier amplitude spectrum to measure the compactness of a signal and using a coarse-to-fine strategy to speed up the searching process.
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Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains
Ahmet Serbes,Lutfiye Durak +1 more
TL;DR: In this paper, the authors presented a method of alternating projections onto convex sets in optimum fractional Fourier domains for signal and image recovery, where the incomplete signal is projected onto different convex set consecutively to restore the missing part.
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Sliding Discrete Linear Canonical Transform
Yan-Nan Sun,Bing-Zhao Li +1 more
TL;DR: This paper introduces a scheme for the single-point DLCT, which can effectively calculate a single or a few linear canonical spectra, and presents two methods to assess performance with regard to computational complexity and precision and to show the correctness of the derived results.
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A Novel Approach to ECG R-Peak Detection
TL;DR: This paper demonstrates a new kind of ECG denoising algorithm based on self-convolution window (SCW) concept which outperformed the results of well-established window-based filters (Hamming and Kaiser) in terms of reduced false negative, false positive, and error rate.