DISCRETE INTEGER MODEL OF COMPLEX TIME-DIVISION SIGNALS WITH A PERIODIC STRUCTURE
DOI:
https://doi.org/10.26906/SUNZ.2026.3.172Keywords:
complex time-division signals, periodic structure, discrete integer model, linear Diophantine equation, coprime numbers, set of discrete positions, pulse overlap\Abstract
The determination of approaches to the analytical synthesis of ensembles of complex timedivision signals without the use of a search-and-correction procedure is relevant for reducing the computational complexity of synthesis of complex time-division signals with a periodic structure. Subject of the study: a discrete integer model of complex time-division signals with a periodic structure and conditions for determining the cardinality of the set of discrete positions of the ensemble and achieving no more than one pulse overlap. Objective: development of a discrete integer model of complex time-division signals with a periodic structure and establishment of conditions based on this model for determining the cardinality of the set of discrete positions of the ensemble and achieving no more than one pulse overlap for each mutual discrete shift of signals. Research tasks: to develop a discrete integer model of complex time-division signals with a periodic structure; to determine the cardinality of the set of discrete positions of the ensemble; to determine the conditions for achieving no more than one pulse overlap for each mutual discrete shift of signals. Methods. The methods of discrete integer modeling and the apparatus of linear Diophantine equations were applied. Results. The mutual coprimality of the numbers of pulses in a pair of signals is a necessary and sufficient condition for the existence of no more than one integer solution of a linear Diophantine equation and the occurrence of no more than one pulse overlap for any mutual discrete shift. Conclusions. The minimum cardinality of the set of discrete positions for a pair of signals is determined as the least common multiple of the numbers of pulses in this pair, and for an ensemble as the maximum of such values obtained for all pairs of signals, which ensures the same duration of ensemble signals and constant integer pulse placement steps.Downloads
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