Regular Section
Parameterization of Perfect Sequences of Real Numbers
2011 年 E94.A 巻 6 号 p. 1401-1407
詳細
2011 年 E94.A 巻 6 号 p. 1401-1407
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.
