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A matrix theory proof of the discrete convolution theorem

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1 Author(s)
Hunt, B. ; University of California, Los Alamos Scientific Laboratory, Los Alamos, NM, USA

In this paper we prove the discrete convolution theorem by means of matrix theory. The proof makes use of the diagonalization of a circulant matrix to show that a circular convolution is diagonalized by the discrete Fourier transform. The diagonalization of the circular convolution shows that the eigenvalues of a circular convolution operator are identical with the discrete Fourier frequency spectrum.

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Audio and Electroacoustics, IEEE Transactions on  (Volume:19 ,  Issue: 4 )