Results 241 to 250 of about 40,269 (290)

Fractional discrete Fourier transforms

Optics Letters, 1996
Direct calculation of fractional Fourier transforms from the expressions derived for their optical implementation is laborious. An extension of the discrete Fourier transform would have only O(N(2)) computational complexity. We define such a system, offer a general way to compute the fractional discrete Fourier transform matrix, and numerically ...
Z T, Deng, H J, Caulfield, M, Schamschula   +2 more
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Random fractional Fourier transform

Optics Letters, 2007
We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics.
Zhengjun, Liu, Shutian, Liu
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Fractional fourier transform: photonic implementation

Applied Optics, 1994
The family of fractional Fourier transforms permits presentation of a temporal signal not only as a function of time or as a pure frequency function but also as a mixed time and frequency function with a continuous degree of emphasis on time or on frequency features.
A W, Lohmann, D, Mendlovic
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Fractional Fourier Transform

2020
This chapter focuses on theory and implementation of fractional Fourier transform (FrFT). FrFT is a wide spread time-frequency tool. The advantages of FrFT domain signal processing has been presented. Various definitions of discrete fractional Fourier transform (DFrFT) has been reviewed and their digital implementation is also explained in detail.
Prajna Kunche, N. Manikanthababu
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Fractional Fourier transformers through reflection

Journal of the Optical Society of America A, 2002
We show that an arbitrary paraxial optical system, compounded with its reflection in an appropriately warped mirror, is a pure fractional Fourier transformer between coincident input and output planes. The geometric action of reflection on optical systems is introduced axiomatically and is developed in the paraxial regime. The correction of aberrations
Kurt Bernardo, Wolf, Guillermo, Krötzsch   +1 more
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Adaptive harmonic fractional Fourier transform

IEEE Signal Processing Letters, 1999
A novel adaptive harmonic fractional Fourier transform is proposed for analysis of voiced speech signals. It provides a higher concentration than STFT and avoids the cross interference components produced by the Wigner-Ville distribution and other bilinear representation. The proposed method rotates the base tone and harmonics in time-frequency domain.
null Fang Zhang, null Yan Qiu Chen, null Guoan Bi   +2 more
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Fractional Fourier–Jacobi type transform

ANNALI DELL'UNIVERSITA' DI FERRARA, 2020
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Coincidence subwavelength fractional Fourier transform

Journal of the Optical Society of America A, 2006
The coincidence subwavelength fractional Fourier transforms (FRTs) with entangled photon pairs and incoherent light radiation are introduced as an extension of the recently introduced coincidence FRT. Optical systems for implementing the coincidence subwavelength FRTs are designed.
Yangjian, Cai, Qiang, Lin, Shi-Yao, Zhu
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On Namias's Fractional Fourier Transforms

IMA Journal of Applied Mathematics, 1987
\textit{V. Namias} [J. Inst. Math. Appl. 25, 241-265 (1980; Zbl 0434.42014)] developed a theory of fractional powers for the Fourier transform and obtained a number of fractional formulae which he used to solve several types of Schrödinger equation. In this paper the authors attempt to provide the necessary mathematical framework for Namias' idea in ...
McBride, A. C., Kerr, F. H.
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The fractional Fourier–Jacobi wavelet transform

The Journal of Analysis, 2023
The main objective of this study is to define the fractional Jacobi translation and fractional Jacobi convolution, as well as to analyze the fractional Fourier-Jacobi wavelet transform and its fundamental properties. Additionally, an inversion formula and a Parseval relation for the continuous fractional Fourier-Jacobi wavelet transform are derived.
Othman Tyr, Faouaz Saadi
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