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Proceedings of the International Conference on Advances in Computing, Communications and Informatics, 2012
The Fractional Fourier transform (FRFT), which provides generalization of conventional Fourier Transform was introduced many years ago in mathematics literature by Namias. In this paper, definition, properties of fractional Fourier transform and its relationship with other transforms is discussed.
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The Fractional Fourier transform (FRFT), which provides generalization of conventional Fourier Transform was introduced many years ago in mathematics literature by Namias. In this paper, definition, properties of fractional Fourier transform and its relationship with other transforms is discussed.
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Adaptive harmonic fractional Fourier transform
IEEE Signal Processing Letters, 1999A 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.
Feng Zhang, Yan Qiu Chen, Guoan Bi
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The hopping discrete fractional Fourier transform
Signal Processing, 2021Abstract The discrete fractional Fourier transform (DFrFT) is a powerful signal processing tool for non-stationary signals. Many types of DFrFT have been derived and successful used in different areas. However, for real-time applications that require recalculating the DFrFT at each or several samples, the existing discrete algorithms aren’t the ...
Yu Liu 0033 +3 more
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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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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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A Comprehensive Survey on Fractional Fourier Transform
Fundamenta Informaticae, 2017The Fractional Fourier transform (FRFT) is a relatively novel linear transforms that is a generalization of conventional Fourier transform (FT). FRFT can transform a particular signal to a unified time-frequency domain. In this survey, we try to present a comprehensive investigation of FRFT.
Yudong Zhang 0001 +6 more
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The fractional Fourier–Jacobi wavelet transform
The Journal of Analysis, 2023The 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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Beam analysis by fractional Fourier transform
Optics Letters, 2001A method of spatial modal decomposition for optical beams by fractional Fourier transform, and its practical implementation with reduced complexity by use of modal interleavers, are discussed.
X, Xue, H, Wei, A G, Kirk
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On the relationship between the Fourier and fractional Fourier transforms
IEEE Signal Processing Letters, 1996In recent years, the fractional Fourier transform has been the focus of many research papers. In this letter, we show that the fractional Fourier transform is nothing more than a variation of the standard Fourier transform and, as such, many of its properties, such as its inversion formula and sampling theorems, can be deduced from those of the Fourier
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Random Discrete Fractional Fourier Transform
IEEE Signal Processing Letters, 2009In this letter, a new commuting matrix with random discrete Fourier transform (DFT) eigenvectors is first constructed. A random discrete fractional Fourier transform (RDFRFT) kernel matrix with random DFT eigenvectors and eigenvalues is then proposed.
Soo-Chang Pei, Wen-Liang Hsue
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A unified framework for the fractional Fourier transform
IEEE Transactions on Signal Processing, 1998The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is ...
CARIOLARO, GIANFRANCO +3 more
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