The method of application of the theory of spectral schedules, theory of moments and statistical-probabilistic methods of processing of the digital information received at preparation of sportsmen for competitive activity, in particular at data processing of heart rate (heart rate) is offered in the work. The paper shows the relationship of the moments of the distribution function with the generalized spectra of orthogonal decompositions, considers the question of determining the sample size to obtain research results. References Pianylo, Ya. D. (2011). Proektsiino-iteratsiini metody rozviazuvannia priamykh ta obernenykh zadach perenosu. Lviv: Splain. Bat, M. (1980). Spektralnyi analiz v geofizike. Moskva. Nedra. Gold, B., Reider, CH. (1973). TSifrovaia obrabotka signalov. Moskva. Sov. radio. Suetin, P. K. (2005). Klassicheskie ortogonalnye mnogochleny 3-e izd. pererab. i dop. M. FIZMATLIT. Dzhekson, D. (1948). Riady fure i ortogonalnye polinomy. Perevod s angliiskogo. Gosudarstvennoe izdatelstvo inostrannoi literatury. Matsko, I. Y., Yavorskyi, I. M., Yuzefovych, R. M., Semenov, P. O. (2018). Statystychnyi vektorno-tenzornyi analiz vibratsii tsentryfuhy z rozvynutym defektom obertovoho vuzla. Fizyko-khimichna mekhanika materialiv, 2, 140-147. Morozova, H. V., Sukharkova, O. I. (2012). Identyfikatsiia fihur na ploshchyni za dopomohoiu tsentralnykh momentiv yikh zobrazhen. Prykladna heometriia ta inzhenerna hrafika, 90, 200-205. Avramenko, V. I., Karimov, I. K. (2013). Teoriia ymovirnostei i matematychna statystyka : navch. posibnyk 2-he vyd., pererob. i dop.Dniprodzerzhynsk : DDTU. Gilmore, J. F., Pemberton, W. B. (1984). A suivery of aircraft classification algorithms. 7th Int. Conf. On PR., Montreal, 559-562. Wolf, S., Louvion, J. R. (1979). Considerations sur les formes: pseudo symetrie representation. 2e congres AFCET-IRIA/ Reconnassance des Formes et Intelligence Artificielle, Toulouse. 381-387. Dudani, J. A., Breeding, K. J. (1997). Aircraft identification by moments invariants. IEEE Trans. On Computers. Hilmor, Dzh. F., Pemberton, W. B. Nabir alhorytmiv klasyfikatsii litakiv. 7th Int. Konf. Pro PR., Monreal, 559-562. Volf, S., Luvion, Dzh. R. (1979). Rozghliad sur les formes: psevdosymetrychne predstavlennia. 2e konhresy AFCET-IRIA / Reconnassance des Formes et Intelligence Artificielle, Tuluza. 381-387. Dudani, Zh. A. (1997). Identyfikatsiia litaka za momentamy invariantiv. IEEE Trans. Pro kompiutery.