The research achievements of perfect correlation signal during decades are particularly surveyed in this paper. These signals have abroad been applied in modern communication, radar, sonar, navigation, space ranging and controlling, and electronic antagonism systems. It is one of objects researching perfect discrete signal for more perfect discrete signals with good correlation character to be obtained for engineering application.Based on the theory research achievements of the perfect binary array pairs, the quasi-perfect binary array pair and the double quasi-perfect binary array pair are defined in this paper. Their properties, Fourier spectrum characters and existing necessary conditions are proved and given out. By means of these conditions, computer searches out many quasi-perfect and double quasi-perfect binary array pairs with small sizes. The composite construction methods for quasi-perfect and double quasi-perfect binary array pairs are studied. And another construction methods for perfect and quasi-perfect binary array pairs are presented with the help of the relationships among the perfect, quasi-perfect and double quasi-perfect binary array pairs. On the other hand, a new kind of discrete signal is presented in this paper, which is the punctured binary sequence pair and the punctured binary array pair. The entire theory systems of the punctured binary sequence pair and the punctured binary array pair are built, which include the perfect punctured binary sequence pair theory, the perfect punctured binary array pair theory, the quasi-perfect and double quasi-perfect binary array pair theory, and the punctured binary complementary sequence pair theory. The punctured binary sequence pair, perfect punctured binary sequence pair and odd-periodic perfect punctured binary sequence pair are defined. Their transform properties and their existing combinatorial admissibility conditions are studied. By means of these properties and conditions, many perfect and odd-periodic perfect binary sequence pairs are searched out. The construction method for the perfect punctured binary sequence pair is presented with the help of the pseudorandom binary sequence. The relationships among perfect binary sequence, perfect and odd-periodic perfect punctured binary sequence pairs are studied. The construction methods for perfect punctured binary sequence pair are presented, one is called the periodic product, and another is with the help of the relationship between perfect and odd-perfect punctured binary sequence pairs. The punctured binary array pair, punctured balance coefficient, perfect and partial periodic perfect punctured binary array pair are defined. The transform properties, Fourier spectrum character and existing necessary combinatorial admissibility conditions of perfect punctured binary array pair are studied. With the help of these properties and conditions, computer searches out many perfect punctured binary array pairs. About the construction methods for perfect punctured binary array pair, we particularly study the methods of constructing perfect punctured binary array pair with two dimension sizes, which include the periodic product between perfect binary array and perfect punctured binary array pair, the kronecker product between the perfect sequence pair and partial periodic perfect punctured binary array pair, and the folding methods between the perfect punctured sequence pair and perfect punctured binary array pair. The quasi-perfect and double quasi-perfect punctured binary array pairs are defined. Their properties and Fourier spectrum characters are studied. The existing combinatorial admissibility conditions are presented. With the help of these conditions, computer efficiently searches out many quasi-perfect and double quasi-perfect punctured binary array pairs. The relationships among perfect punctured binary array pair, quasi-perfect and double quasi-perfect punctured binary array pair is presented. Specially, when first and second dimension period of the punctured binary ar