Issues of temporary search of periodic and aperiodic complex discrete signals are considered. The focus is on periodic (cyclic) synchronization. The problem of selecting synchronised signals and optimizing the methods of their processing is solved, which makes it possible to significantly simplify the search compared to the method of complete search. Generalizations of dichotomous methods for fast search sequences are described. Rapid spectral transformations are used to simplify synchronization and decoding procedures. The synchronization problem is solved when processing only a part of the periodic signal - the information system. Effective methods of information transfer are proposed simultaneously with the synchronization procedure. A significant place in the book is given to various methods of block synchronization of cyclic codes. Methods of aperiodic synchronization are considered, which are built both on the basis of methods of periodic synchronization, and directly, for example, by means of synchronization along the information system. The basic concepts of the theory of computational complexity are presented, and with its help, the previously considered search methods are evaluated and compared during their hardware and software implementation. For scientists; can be useful to engineers-developers of radio communication, radar and radio navigation systems.