Discrete fourier transform tensors and their ranks

Research output: Contribution to journalArticle

Abstract

We introduce a tensor generalization of the matrix discrete Fourier transform (DFT) which we call the collapsed DFT (CDFT) tensor. The CDFT tensor is different from the standard even order DFT tensor (except when the order is two). We study the action and compute the rank of the DFT tensor. Our main results for the CDFT tensors include their action, monotonicity of rank with respect to order, bounds on rank, and exact computation of rank of third order CDFT tensors when the dimension of the underlying space is a prime number.

Original languageEnglish (US)
Pages (from-to)1010-1027
Number of pages18
JournalSIAM Journal on Matrix Analysis and Applications
Volume38
Issue number3
DOIs
StatePublished - 2017

Keywords

  • Discrete Fourier transforms
  • Tensor ranks
  • Tensors

ASJC Scopus subject areas

  • Analysis

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