Application of block matrix theory to obtain the inverse transform of the vector-valued DFT

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Abstract

We study the vector-valued discrete Fourier transform (vector-valued DFT) and its inverse transform, the vector-valued DFT inversion, through its block matrix representation. These transforms are defined for N- periodic signals, taking values in CD. The vector-valued DFT is a gen- eralization of classical discrete Fourier transform definition. The goal of this paper is present necessary and sufficient new conditions to vector- valued DFT inversion, and so, to make a perfect recovery of original signal.

Original languageEnglish
Pages (from-to)2567-2577
Number of pages11
JournalApplied Mathematical Sciences
Volume9
Issue number49-52
DOIs
StatePublished - 2015

Keywords

  • DFT frames
  • DFT matrix
  • Vector-valued DFT
  • Vector-valued DFT inversion

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