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Research articles

ScienceAsia 40S(2014): 51-57 |doi: 10.2306/scienceasia1513-1874.2014.40S.051

Computation of a real eigenbasis for the Simpson discrete Fourier transform matrix

Virath Singha, Pravin Singha,*

ABSTRACT:     In this paper, we demonstrate the usefulness of the duality property by using it to determine the spectrum of the Simpson discrete Fourier transform (SDFT) matrix of dimension N×N, where Nequiv2±od4, in finding an expression for the minimal polynomial. We determine the eigenvalues and their corresponding multiplicities. The SDFT matrix is diagonalizable. Thus there exists a basis for the underlying vector space consisting of eigenvectors. In light of this, we construct an eigenbasis for each subspace associated with each of the eight distinct eigenvalues.

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a School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa

* Corresponding author, E-mail: singhprook@gmail.com

Received 13 Feb 2014, Accepted 0 0000