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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
Discrete matrix model for synthesis of mutual intensity functions
TL;DR: By singular value decomposition of the mutual intensity matrix, an equivalent representation is obtained which reduces this quadratic problem of obtaining light of a desired mutual intensity from a light source of given mutual intensity by employing a linear optical system.
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Effect of Diffraction on Wigner Distributions of Optical Fields and how to Use It in Optical Resonator Theory. I -- Stable Resonators and Gaussian Beams
Pierre Pellat-Finet,Eric Fogret +1 more
TL;DR: In this article, a theory of stable optical resonators and Gaussian beams is developed on the basis of this property, including waist existence and related formulae, and naturally introducing the Gouy phase.
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Denoising of lightning electric field signals using fractional Fourier transform
TL;DR: In this paper, the results of applying the fractional Fourier transform (FRFT) as an alternative technique to reduce the presence of noise and also of undesired signal components within a set of electric field signatures are presented.
Proceedings ArticleDOI
Fractional Fourier transform with pulse inversion for second harmonic pulse compression
Muhammad Arif,Steven Freear +1 more
TL;DR: In this article, a fractional Fourier transform (FrFT) with pulse inversion is proposed for the second harmonic pulse compression in ultrasound harmonic imaging with chirp coded excitation, which shows a 13.5% improvement in the mainlobe width with comparable peak sidelobe levels, when compared with the conventional HMF technique.
Journal ArticleDOI
Optical image asymmetric cryptosystem using fingerprint based on iterative fraction Fourier transform
TL;DR: A novel asymmetric cryptosystem for optical image is proposed using fingerprint based on iterative fractional Fourier transform, which is applicable for information authentication because the fingerprint is used both in encryption and decryption approach.