V. I. Shetinin - Ph.D. (Eng.), Associate Professor, Odintsovskiy Humanities Institute (Moscow region)
Yu. A. Kavin - Ph.D. (Eng.), Associate Professor, Professor, Odintsovskiy Humanities Institute (Moscow region)
L. S. Pritchina - Ph.D. (Eng.), Associate Professor, Professor, Odintsovskiy Humanities Institute (Moscow region)

The synthesis of the two varieties of optimal discreet signals singular ensembles is made on the basis of linear decomposition filters. One of the ensembles is based on perfect difference sets involving the mathematical apparatus of the complex expanded Galua fields. The discreet signals of such an ensemble are optimal, and the ultra broadband signals synthesized on discreet signals will have a unit level of side lobes. As the number of pulses in a sequence and the number of sequences in an ensemble are the same, signals on such a basis are convenient to use for data transfer coded with, e.g., WalshAdamar matrix. The patterns of the other ensemble variety are synthesized on a difference sets basis. The number of sequence pulses is fixed and is equal to four; the number of ensemble sequences is a power of four. As in the previous case, frequency-shift keyed ultra broadband signals with four pulses on each frequency can be built on the ensemble basis, an additional spectrum expansion of such a signal in comparison with the signals of the first variety can be provided, as well as the problem of super resolution can be solved with application of such signals. It has been shown that the spectrum expansion is also possible for the first variety of signals based on the optimal discreet patterns if decimation is applied to the pulses of each frequency component. This approach provides for fast transformation methods in signal processing.