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

Pablo Soto-Quiros

doi:10.12988/ams.2015.52125

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

Pablo Soto-Quiros

Escuela de Matemática

Adelaide University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 C^D. 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 language	English
Pages (from-to)	2567-2577
Number of pages	11
Journal	Applied Mathematical Sciences
Volume	9
Issue number	49-52
DOIs	https://doi.org/10.12988/ams.2015.52125
State	Published - 2015

Keywords

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

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10.12988/ams.2015.52125

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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.",

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KW - Vector-valued DFT inversion

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

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Keywords

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