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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
The Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform
TL;DR: In this article, the Wigner-Ville distribution associated with the quaternionic offset linear canonical transform (WVD-QOLCT) is defined and the Poisson summation formula for the WVD is given.
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Efficient ray tracing through aspheric lenses and imperfect bokeh synthesis
TL;DR: An efficient ray‐tracing technique to render bokeh effects produced by parametric aspheric lenses and a numerical root‐finding approach, which uses tight proxy surfaces to ensure a good initialization and convergence behavior is proposed.
Journal ArticleDOI
Joint time-frequency offset detection using the fractional Fourier transform
TL;DR: The approach is particularly designed for analysing measured signals with different onset time (travel time) and frequency shift (Doppler), as compared to a given signal model.
Journal ArticleDOI
Sampling of fractional bandlimited signals associated with fractional Fourier transform
Deyun Wei,Qiwen Ran,Yuan-Min Li +2 more
TL;DR: It is shown that the sampling expansion for fractional bandlimited signals with FRFT is a special case of Parseval’s relation for complex FRFS.
Signature 기반의 얼굴 검출 기법
TL;DR: The face detection method using its signature is presented, where features extracted from the signature are projected to the eigenspace using BDFs to decide whether they are of a face or not using the Bayesian decision rule.