General solution for orthogonal periodic real‐number sequences
General solution for orthogonal periodic real‐number sequences
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正交周期实数序列的通解
DOI：
10.1002/ecja.4410690506
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
Y. Tanada
中科院分区：
文献类型：
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作者：
Y. Tanada
本文针对扩频通信中的应用，给出了具有零旁瓣自相关函数的实数周期序列的一般解。通过用傅里叶级数表示自相关函数，并利用分量得到通解。该解包含相常数。也就是说，在序列为实数、相位常数为奇函数的情况下，通过离散傅里叶变换将序列与相位常数联系起来。然而，当相位常数仅取{O，π}中的值时，相位常数是偶(=奇)函数，并且序列是偶函数。从通解出发，证明了由N阶序列移位得到的N个序列是正交的。给出了当相位常数固定为φk E{0，φ}，φk=2πk3/N(k=0，1，‥，N-L)和当其连续为PHIV；1=-φN-1=θ时，该序列的一个例子。该通解为各种伪噪声序列的计算提供了依据。
This paper shows the general solution for the real-number periodic sequence with an autocorrelation function with zero side lobe, aiming at the application to the spread-spectrum communication. The general solution is derived by representing the autocorrelation function by a Fourier series and utilizing the components. The solution contains the phase constant. In other words, the sequence and the phase constant are related through the discrete Fourier transform Under the condition that the seqeunce is real, the phase constant is an odd function. However, when the phase constant takes only the value in {O, π}, the phase constant is an even (= odd) function, and the sequence is an even function. From the general solution, it is shown that N sequences obtained by shifting a sequence of order N are orthogonal. An example of the sequence is shown for the case where the phase constant is fixed as φ k E {0, φ }, φk = 2πk3/N (k = 0, 1, ‥, N - l), and for the case where it is continuous as Phiv;1=- φ N-1= θ. The general solution provides a basis for calculating various kinds of pseudonoise sequences.