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Discrete Chrestenson transform

М. С. Беспалов

Open publisher page 10 citations

Abstract

The discrete Chrestenson-Kronecker transform is a linear transform whose matrix is a Kronecker power of the matrix of the discrete Fourier transform. The matrix of the discrete Chrestenson-Lévy transform is represented as a power of the matrix of the discrete Fourier transform with respect to a new direct product of matrices. We study properties of and analyze fast algorithms for these two main kinds of the discrete Chrestenson transform. We consider properties of and construction methods for other types of the discrete Chrestenson transform.

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What this paper is about

The discrete Chrestenson-Kronecker transform is a linear transform whose matrix is a Kronecker power of the matrix of the discrete Fourier transform. The matrix of the discrete Chrestenson-Lévy transform is represented as a power of the matrix of the discrete Fourier transform with respect to a new direct product of matrices. We study properties of and analyze fast algorithms for these two main kinds of the discrete Chrestenson transform. We consider properties of and construction methods for other types of the discrete Chrestenson transform.

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Available abstract

The discrete Chrestenson-Kronecker transform is a linear transform whose matrix is a Kronecker power of the matrix of the discrete Fourier transform. The matrix of the discrete Chrestenson-Lévy transform is represented as a power of the matrix of the discrete Fourier transform with respect to a new direct product of matrices. We study properties of and analyze fast algorithms for these two main kinds of the discrete Chrestenson transform. We consider properties of and construction methods for other types of the discrete Chrestenson transform.

Key concepts: Discrete Fourier transform (general), Discrete sine transform, Discrete Hartley transform, Mathematics, Kronecker product, Fractional Fourier transform, DFT matrix, Hartley transform

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