Parameterization of Perfect Sequences of Real Numbers
Summary :
A perfect sequence is a sequence having an impulsive autocorrelation function. Perfect sequences have several applications, such as CDMA, ultrasonic imaging, and position control. A parameterization of a perfect sequence is presented in the present paper. We treat a set of perfect sequences as a zero set of quadratic equations and prove a decomposition law of perfect sequences. The decomposition law reduces the problem of the parameterization of perfect sequences to the problem of the parameterization of quasi-perfect sequences and the parameterization of perfect sequences of short length. The parameterization of perfect sequences for simple cases and quasi-perfect sequences should be helpful in obtaining a parameterization of perfect sequences of arbitrary length. According to our theorem, perfect sequences can be represented by a sum of trigonometric functions.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.6 pp.1401-1407
- Publication Date
- 2011/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E94.A.1401
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Keyword
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Takao MAEDA, Takafumi HAYASHI, "Parameterization of Perfect Sequences of Real Numbers" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 6, pp. 1401-1407, June 2011, doi: 10.1587/transfun.E94.A.1401.
Abstract: A perfect sequence is a sequence having an impulsive autocorrelation function. Perfect sequences have several applications, such as CDMA, ultrasonic imaging, and position control. A parameterization of a perfect sequence is presented in the present paper. We treat a set of perfect sequences as a zero set of quadratic equations and prove a decomposition law of perfect sequences. The decomposition law reduces the problem of the parameterization of perfect sequences to the problem of the parameterization of quasi-perfect sequences and the parameterization of perfect sequences of short length. The parameterization of perfect sequences for simple cases and quasi-perfect sequences should be helpful in obtaining a parameterization of perfect sequences of arbitrary length. According to our theorem, perfect sequences can be represented by a sum of trigonometric functions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1401/_p
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@ARTICLE{e94-a_6_1401,
author={Takao MAEDA, Takafumi HAYASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Parameterization of Perfect Sequences of Real Numbers},
year={2011},
volume={E94-A},
number={6},
pages={1401-1407},
abstract={A perfect sequence is a sequence having an impulsive autocorrelation function. Perfect sequences have several applications, such as CDMA, ultrasonic imaging, and position control. A parameterization of a perfect sequence is presented in the present paper. We treat a set of perfect sequences as a zero set of quadratic equations and prove a decomposition law of perfect sequences. The decomposition law reduces the problem of the parameterization of perfect sequences to the problem of the parameterization of quasi-perfect sequences and the parameterization of perfect sequences of short length. The parameterization of perfect sequences for simple cases and quasi-perfect sequences should be helpful in obtaining a parameterization of perfect sequences of arbitrary length. According to our theorem, perfect sequences can be represented by a sum of trigonometric functions.},
keywords={},
doi={10.1587/transfun.E94.A.1401},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Parameterization of Perfect Sequences of Real Numbers
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1401
EP - 1407
AU - Takao MAEDA
AU - Takafumi HAYASHI
PY - 2011
DO - 10.1587/transfun.E94.A.1401
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2011
AB - A perfect sequence is a sequence having an impulsive autocorrelation function. Perfect sequences have several applications, such as CDMA, ultrasonic imaging, and position control. A parameterization of a perfect sequence is presented in the present paper. We treat a set of perfect sequences as a zero set of quadratic equations and prove a decomposition law of perfect sequences. The decomposition law reduces the problem of the parameterization of perfect sequences to the problem of the parameterization of quasi-perfect sequences and the parameterization of perfect sequences of short length. The parameterization of perfect sequences for simple cases and quasi-perfect sequences should be helpful in obtaining a parameterization of perfect sequences of arbitrary length. According to our theorem, perfect sequences can be represented by a sum of trigonometric functions.
ER -
English
