Parameterization of Perfect Sequences of Real Numbers

Takao MAEDA  Takafumi HAYASHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.6   pp.1401-1407
Publication Date: 2011/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1401
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
perfect sequence,  parameterization,  zero-correlation zone,  

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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.