COMPLEMENTARY SERIES
COMPLEMENTARY SERIES
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DOI：
10.1109/tit.1961.1057620
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发表时间：
1961-01-01
期刊：
影响因子：
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通讯作者：
GOLAY, MJE
中科院分区：
文献类型：
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作者：
GOLAY, MJE
一组互补序列被定义为两种元素的一对等长的有限序列，它们具有这样的性质：在一个序列中具有任何一个给定间隔的相似元素的对数等于在另一个序列中具有相同给定间隔的不同元素的对数。(For例如，两个系列1001010001和1000000110分别具有三对相同和三对不同的相邻元件，四对相同和四对不同的交替元件，等等，用于所有可能的分离。这些序列最初是与多缝光谱的光学问题联系起来设想的，在通信工程中也有可能应用，因为当这些序列的两种元素被取为+1和-1时，从它们的定义可以立即得出，它们两个各自的自相关序列的和在任何地方都是零，除了中心项。几个命题相对于这些系列，其允许的数量的元素，并证明其合成。
A set of complementary series is defined as a pair of equally long, finite sequences of two kinds of elements which have the property that the number of pairs of like elements with any one given separation in one series is equal to the number of pairs of unlike elements with the same given separation in the other series. (For instance the two series, 1001010001 and 1000000110 have, respectively, three pairs of like and three pairs of unlike adjacent elements, four pairs of like and four pairs of unlike alternate elements, and so forth for all possible separations.) These series, which were originally conceived in connection with the optical problem of multislit spectrometry, also have possible applications in communication engineering, for when the two kinds of elements of these series are taken to be +1 and -1, it follows immediately from their definition that the sum of their two respective autocorrelation series is zero everywhere, except for the center term. Several propositions relative to these series, to their permissible number of elements, and to their synthesis are demonstrated.