Research For Perfect Discrete Signal

The perfect discrete single and its design method play an important part in the optimizing design in the area of modernistic communication, radar, sonar, navigation, space ranging and controlling and electronically antagonism systems. It is of theoretical and application importance to study all kinds of sequence properties. An abundance of research results were published through several decades and further researches have been carried out regarding these theories. The design rules of the perfect discrete single usually include periodic correlation and aperiodic correlation, dyadic correlation, etc. The goal of this paper is to study the perfect discrete singles basing on periodic correlation and dyadic correlation. After analyzing and integrating the actuality of the kind of perfect singles in internal and external, this paper studies it further.The designs of the perfect discrete single based on the rule of periodic correlative function are discussed in the first part of the paper. Firstly, the concept of sequence pairs and the some properties of the sequence pairs are introduced, which lays the foundation for later work. Secondly, according to almost perfect autocorrelation sequences, the theory of almost perfect auto- correlation sequence pairs is presented. Some characters and Fourier spectrum characters of the almost perfect autocorrelation sequence pairs are discussed, and the necessary conditions of existences of the almost perfect auto- correlation sequence pairs are given. Lastly, the concept of families of almost perfect periodic complementary sequence pairs is given on the basis of the almost perfect autocorrelation sequence pairs. The method on constructing families of almost perfect periodic complementary sequence pairs is given and proved. The designs of the perfect discrete single based on the rule of dyadic correlative function are discussed in the secondly part of the paper. The study of Bent functions takes the place of the study binary dyadic codes, because they are equipollent. Firstly, the concept of the families of Bent complemen- tary function pairs is defined, and several transform properties are given and proved. The equivalent relation between the families of Bent complementary function pairs and the families of dyadic complementary sequence pairs is discussed, so are the families of Hadmard complementary array pairs. Then, these constructions of the families of Bent complementary function pairs that are based on some special arrays, for example orthogonal column arrays and dyadic perfect arrays, are studied. In the end, Bent function pair mates are given, which increase the constructions of the families of Bent complementary function pairs.