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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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Proceedings ArticleDOI
Applications of Rotational Time-Frequency Transforms To Radar Imaging of Moving Targets
TL;DR: The basic concept of rotational time-frequency transforms is introduced, some properties of the fractional Fourier transform are discussed, a bilinear generalized-marginal time- frequencies transform is described, and the Radon transform is presented for line feature detection and estimation.
Journal ArticleDOI
Coherent diffraction imaging based on iterative fractional Fourier transform
TL;DR: This method overcomes the limitations of the same-kind methods which require a prior knowledge of the accurate order of fractional Fourier transform, and converges faster and achieves less error.
Journal ArticleDOI
Fractional order processing of quartz crystal microbalance based dna biosensor signals
Anhong Zhou,YangQuan Chen +1 more
TL;DR: In this article, two fractional order signal processing techniques, namely, fractional Fourier transform (FrFT) and rescaled range statistical analysis (R/S analysis), are applied to analyze the QCM signals.
Proceedings Article
Higher order modulation and the efficient sampling algorithm for time variant signal
TL;DR: The proposed sampling algorithm can minimize the area of a signal in the time-frequency domain and much reduce the number of sampling points and is especially efficient for sampling a time variant signal, such as the voice of an animal and the speech signal.
Proceedings ArticleDOI
A novel spectrum reconstruction algorithm based on FrFT for multiple azimuth beam SAR
TL;DR: Based on the theory of the paired echoes, the influence of periodic non- uniform sampling for SAR imaging has been derived and signal model of non-uniformly sampling in azimuth direction has been established and detailed analysis of spectrum reconstruction algorithm in the fractional Fourier domain has been performed.