Generalizing the Hadamard Matrix Using the Reverse Jacket Matrix

Seung-Rae LEE; Wook Hyun KWON; Koeng-Mo SUNG

Generalizing the Hadamard Matrix Using the Reverse Jacket Matrix

Seung-Rae LEE, Wook Hyun KWON, Koeng-Mo SUNG

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In this paper, the previous definition of the Reverse Jacket matrix (RJM) is revised and generalized. In particular, it is shown that the inverse of the RJM can be obtained easily by a constructive approach similar to that used for the RJM itself. As new results, some useful properties of RJMs, such as commutativity and the Hamiltonian symmetry appearing in half the blocks of a RJM, are shown, and also 1-D fast Reverse Jacket transform (FRJT) is presented. The algorithm of the FRJT is remarkably efficient than that of the center-weighted Hadamard transform (CWHT). The FRJT is extended in terms of the Kronecker products of the Hadamard matrix. The 1-D FRJT is applied to the discrete Fourier transform (DFT) with order 4, and the N-point DFT can be expressed in terms of matrix decomposition by using 4 4 FRJT.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.10 pp.2732-2743

Publication Date: 2004/10/01

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Type of Manuscript: PAPER

Category: Digital Signal Processing

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Seung-Rae LEE, Wook Hyun KWON, Koeng-Mo SUNG, "Generalizing the Hadamard Matrix Using the Reverse Jacket Matrix" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 10, pp. 2732-2743, October 2004, doi: .
Abstract: In this paper, the previous definition of the Reverse Jacket matrix (RJM) is revised and generalized. In particular, it is shown that the inverse of the RJM can be obtained easily by a constructive approach similar to that used for the RJM itself. As new results, some useful properties of RJMs, such as commutativity and the Hamiltonian symmetry appearing in half the blocks of a RJM, are shown, and also 1-D fast Reverse Jacket transform (FRJT) is presented. The algorithm of the FRJT is remarkably efficient than that of the center-weighted Hadamard transform (CWHT). The FRJT is extended in terms of the Kronecker products of the Hadamard matrix. The 1-D FRJT is applied to the discrete Fourier transform (DFT) with order 4, and the N-point DFT can be expressed in terms of matrix decomposition by using 4 4 FRJT.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_10_2732/_p

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@ARTICLE{e87-a_10_2732,
author={Seung-Rae LEE, Wook Hyun KWON, Koeng-Mo SUNG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Generalizing the Hadamard Matrix Using the Reverse Jacket Matrix},
year={2004},
volume={E87-A},
number={10},
pages={2732-2743},
abstract={In this paper, the previous definition of the Reverse Jacket matrix (RJM) is revised and generalized. In particular, it is shown that the inverse of the RJM can be obtained easily by a constructive approach similar to that used for the RJM itself. As new results, some useful properties of RJMs, such as commutativity and the Hamiltonian symmetry appearing in half the blocks of a RJM, are shown, and also 1-D fast Reverse Jacket transform (FRJT) is presented. The algorithm of the FRJT is remarkably efficient than that of the center-weighted Hadamard transform (CWHT). The FRJT is extended in terms of the Kronecker products of the Hadamard matrix. The 1-D FRJT is applied to the discrete Fourier transform (DFT) with order 4, and the N-point DFT can be expressed in terms of matrix decomposition by using 4 4 FRJT.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Generalizing the Hadamard Matrix Using the Reverse Jacket Matrix
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2732
EP - 2743
AU - Seung-Rae LEE
AU - Wook Hyun KWON
AU - Koeng-Mo SUNG
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2004
AB - In this paper, the previous definition of the Reverse Jacket matrix (RJM) is revised and generalized. In particular, it is shown that the inverse of the RJM can be obtained easily by a constructive approach similar to that used for the RJM itself. As new results, some useful properties of RJMs, such as commutativity and the Hamiltonian symmetry appearing in half the blocks of a RJM, are shown, and also 1-D fast Reverse Jacket transform (FRJT) is presented. The algorithm of the FRJT is remarkably efficient than that of the center-weighted Hadamard transform (CWHT). The FRJT is extended in terms of the Kronecker products of the Hadamard matrix. The 1-D FRJT is applied to the discrete Fourier transform (DFT) with order 4, and the N-point DFT can be expressed in terms of matrix decomposition by using 4 4 FRJT.
ER -