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Synchrosqueezing-Based Short-Time Fractional Fourier Transform
IEEE Transactions on Signal Processing, 2023A novel synchrosqueezing transform to the time-frequency representation based on short-time fractional Fourier transform for strong time-varying signals is proposed in this paper.
Zhichun Zhao, Gang Li
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Fractional Fourier Transform and Transferred CNN Based on Tensor for Hyperspectral Anomaly Detection
IEEE Geoscience and Remote Sensing Letters, 2022Most of the algorithms for hyperspectral anomaly detection (AD) are based on the original spectral signatures which may suffer noise contamination. In recent years, some AD algorithms based on deep learning (DL) and tensor have achieved satisfactory ...
Lili Zhang, Baozhi Cheng
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Fractional Fourier Transform in Time Series Prediction
IEEE Signal Processing Letters, 2022Several signal processing tools are integrated into machine learning models for performance and computational cost improvements. Fourier transform (FT) and its variants, which are powerful tools for spectral analysis, are employed in the prediction of ...
E. Koç, Aykut Koç
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Fractional Fourier Transform Meets Transformer Encoder
IEEE Signal Processing Letters, 2022Utilizing signal processing tools in deep learning models has been drawing increasing attention. Fourier transform (FT), one of the most popular signal processing tools, is employed in many deep learning models.
Furkan Şahinuç, Aykut Koç
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On the extension of the coupled fractional Fourier transform and its properties
Integral transforms and special functions, 2021The coupled fractional Fourier transform is a two-dimensional fractional Fourier transform that depends on two angles that are coupled in such a way that the transform parameters are and It generalizes the two-dimensional Fourier transform and it serves ...
R. Kamalakkannan, R. Roopkumar, A. Zayed
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Novel Short-Time Fractional Fourier Transform: Theory, Implementation, and Applications
IEEE Transactions on Signal Processing, 2020As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable for processing signals whose fractional frequencies vary
Jun Shi +4 more
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Fractional finite Fourier transform
Journal of the Optical Society of America A, 2004We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform.
Nicholas George, Kedar Khare
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Short time coupled fractional fourier transform and the uncertainty principle
Fractional Calculus and Applied Analysis, 2021In this paper, we introduce a short-time coupled fractional Fourier transform ( scfrft ) using the kernel of the coupled fractional Fourier transform ( cfrft ).
R. Kamalakkannan, R. Roopkumar, A. Zayed
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Random fractional Fourier transform
Optics Letters, 2007We 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 discrete Fourier transforms
Optics Letters, 1996Direct 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 ...
Marius P. Schamschula +2 more
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