Fourier matrices and Fourier tensors

Abstract

The Fourier matrix is fundamental in discrete Fourier transforms and fast Fourier transforms. We generalize the Fourier matrix, extend the concept of Fourier matrix to higher order Fourier tensor, present the spectrum of the Fourier tensors, and use the Fourier tensor to simplify the high order Fourier analysis.

Keywords

Fourier matrix / tensor / CP decomposition / Fourier analysis

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