Hermite–Gaussian-Like Eigenvectors of the Discrete Fourier Transform Matrix Based on the Singular-Value Decomposition of Its Orthogonal Projection Matrices

Hanna, M.T.; Seif, N. P.; Ahmed, Waleed Abd El Maguid

doi:10.1109/tcsi.2004.836850

Cited by 44 publications

(14 citation statements)

References 10 publications

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“…Hanna et al [29] claim to find the eigenvectors of the DFT matrix using a similar method. However, they use the ordinary-DFT matrix as a basis to their work, but Serbes and Durak-Ata [28] employs the CDFT matrix.…”

Section: Random Type Dfrft Pei and Hsuementioning

confidence: 99%

DFRFT: A Classified Review of Recent Methods with Its Application

Singh¹,

Saxena²

2013

Journal of Engineering

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In the literature, there are various algorithms available for computing the discrete fractional Fourier transform (DFRFT). In this paper, all the existing methods are reviewed, classified into four categories, and subsequently compared to find out the best alternative from the view point of minimal computational error, computational complexity, transform features, and additional features like security. Subsequently, the correlation theorem of FRFT has been utilized to remove significantly the Doppler shift caused due to motion of receiver in the DSB-SC AM signal. Finally, the role of DFRFT has been investigated in the area of steganography.

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Section: Random Type Dfrft Pei and Hsuementioning

confidence: 99%

DFRFT: A Classified Review of Recent Methods with Its Application

Singh¹,

Saxena²

2013

Journal of Engineering

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“…[54], the orthonormal eigenvectors of F are obtained by applying the singular-value decomposition technique, not by using the matrix S. And the sequential OPA (SOPA) algorithm is presented for generating good Hermite-Gaussian-like eigenvectors of F. According to the spectral theorem, F has the following spectral decomposition,…”

Section: S S Imentioning

confidence: 99%

Research progress on discretization of fractional Fourier transform

Tao

Zhang

Wang

2008

Sci. China Ser. F-Inf. Sci.

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As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform (including 3 main types: linear combination-type; sampling-type; and eigen decomposition-type), and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.fractional Fourier transform, sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform

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“…Pei et alin [17], first proposed the eigen decomposition-based definition of the DFRFT and then Candan et al consolidated this definition [18]. Hanna et al considered generation eigenvectors by the singular value decomposition method and direct batch evaluation [21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm

Sharma¹,

Saxena²,

Singh³

2014

IJCNIS

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Abstract-Encryption along with compression is the process used to secure any multimedia content processing with minimum data storage and transmission. The transforms plays vital role for optimizing any encryptioncompression systems. Earlier the original information in the existing security system based on the fractional Fourier transform (FRFT) is protected by only a certain order of FRFT. In this article, a novel method for encryption-compression scheme based on multiple parameters of discrete fractional Fourier transform (DFRFT) with random phase matrices is proposed. The multiple-parameter discrete fractional Fourier transform (MPDFRFT) possesses all the desired properties of discrete fractional Fourier transform. The MPDFRFT converts to the DFRFT when all of its order parameters are the same. We exploit the properties of multipleparameter DFRFT and propose a novel encryptioncompression scheme using the double random phase in the MPDFRFT domain for encryption and compression data. The proposed scheme with MPDFRFT significantly enhances the data security along with image quality of decompressed image compared to DFRFT and FRFT and it shows consistent performance with different images. The numerical simulations demonstrate the validity and efficiency of this scheme based on Peak signal to noise ratio (PSNR), Compression ratio (CR) and the robustness of the schemes against bruit force attack is examined.

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Hermite–Gaussian-Like Eigenvectors of the Discrete Fourier Transform Matrix Based on the Singular-Value Decomposition of Its Orthogonal Projection Matrices

Cited by 44 publications

References 10 publications

DFRFT: A Classified Review of Recent Methods with Its Application

DFRFT: A Classified Review of Recent Methods with Its Application

Research progress on discretization of fractional Fourier transform

Hybrid Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm

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