The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.
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Shinya MATSUFUJI, Takahiro MATSUMOTO, Pingzhi FAN, "Even-Shift Orthogonal Arrays" in IEICE TRANSACTIONS on Fundamentals,
vol. E95-A, no. 11, pp. 1937-1940, November 2012, doi: 10.1587/transfun.E95.A.1937.
Abstract: The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.1937/_p
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@ARTICLE{e95-a_11_1937,
author={Shinya MATSUFUJI, Takahiro MATSUMOTO, Pingzhi FAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Even-Shift Orthogonal Arrays},
year={2012},
volume={E95-A},
number={11},
pages={1937-1940},
abstract={The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.},
keywords={},
doi={10.1587/transfun.E95.A.1937},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - Even-Shift Orthogonal Arrays
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1937
EP - 1940
AU - Shinya MATSUFUJI
AU - Takahiro MATSUMOTO
AU - Pingzhi FAN
PY - 2012
DO - 10.1587/transfun.E95.A.1937
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2012
AB - The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.
ER -