Method of synthesis of the sequences, possessing ideal autocorrelation functions, has been developed. The review of existing approaches, analytical conclusion of requirements to ideal sequences with considering the necessity to provide low pick-factor of the sequence and low level of side petals of autocorrelation function has been given. Mathematical model and its program embodiment, allowing to generate periodical sequences and assess their properties, have been created on the basis of suggested method. As a result of pursued computational experiments, the sequences with number of symbols from 6 to 4096 have been obtained. It’s been clarified that such sequence can be formed at its any length which has ideal periodic autocorrelation function at pick-factor equal or close to 1. Because suggested sequences have ideal ACF they can be recommended for use in the systems of railway automatics and communication for highly reliable management of train traffic on high-speed trunks as well as in communication systems qua signals in navigating and locational systems, qua signals applied in ultrasound defectoscopy and so on.
random sequences, Chirp signals, spectral numbers, Fourier transform, autocorrelation function, side picks of ACF, circulants, sequence pick-factor
1. Egorov V.V. Vremennaya sinkhronizatsiya v sistemakh svyazi amplitudno-fazomanipulirovannymi signalami [Time synchronization in communication systems with amplitude-phase-shift keyed signals]. Tezisy dokladov nauchno-tekhnicheskoy konferentsii «Povyshenie kachestva i effektivnosti ustroystv sinkhronizatsii v sistemakh svyazi». Rossiyskoe nauchno-tekhnicheskoe obshchestvo radiotekhniki, elektroniki i svyazi im. A.S. Popova. Sektsiya ustroystv sinkhronizatsii. Yaroslavskiy Gosudarstvennyy Universitet, Moskovskiy tekhnicheskiy Universitet svyazi i informatiki, Yaroslavl', 25-27 maya 1993 [Abstracts of the scientific and technical conference "Improving the quality and efficiency of synchronization devices in communication systems" . Russian Scientific and Technical Society of Radio Engineering, Electronics and Communications. A.S. Popov. Synchronization devices section. Yaroslavl State University, Moscow Technical University of Communications and Informatics, Yaroslavl, May 25-27, 1993]. Yaroslavl': RNTORES im. A.S. Popova Publ., 1993, p. 54.
2. Dvornikov V.D. Mnogofaznye posledovatel'nosti s ideal'nymi korrelyatsionnymi svoystvami. Doklady BGUIR [Multiphase sequences with ideal correlation properties. Reports of BSUIR]. 2003 Minsk., Belarus'. 2003. V. 1. I. 1.
3. Khodakovskiy V.A. Sintez signalov s optimal'nymi po urovnyu bokovykh lepestkov avtokorrelyatsionnymi svoystvami [Synthesis of signals with optimal autocorrelation properties in terms of the level of side lobes]. Izvestiya Peterburgskogo universiteta putey soobshcheniya [Proceedings of the Petersburg University of Communications]. 2018, V.15, I. 4, pp. 629-636.
4. David C. Chu. // IEEE Trans. Inform. Theory. 1972. Vol. IT−18, № 3. P. 531–532.
5. Frank R.I., Zadoff S.A. // IRE Trans. Inform. Theory. 1962. Vol. IT−8. Oct. P. 381–382.
6. Heimler R.C. // IRE Trans. Inform. Theory. 1961. Vol. IT−7. Oct. P. 254–257.
7. Khodakovskiy V.A., Lobov S.A. Ob odnom sposobe podavleniya bokovykh lepestkov funktsii avtokorrelyatsii [On one way to suppress the side lobes of the autocorrelation function]. Intellektual'nye tekhnologii na transporte. PGUPS Imperatora Aleksandra I [Intelligent technologies in transport. PGUPS Emperor Alexander I]. 2020, I. 4(24), pp. 46-50.
8. Degtyarev V.G., Khodakovskiy V.A. Mnogokriterial'noe upravlenie vagonami na zheleznodorozhnom transporte [Multi-criteria management of wagons in railway transport]. Intellektual'nye tekhnologii na transporte. PGUPS Imperatora Aleksandra I [Intelligent technologies in transport. PGUPS Emperor Alexander I]. 2016, I. 3(7), pp.14-20.
9. Khodakovskiy V.A. Teorema otschetov i obratnoe ee tolkovanie dlya analiza signalov s ogranichennym spektrom [The sampling theorem and its reverse interpretation for the analysis of signals with a limited spectrum]. Problemy matematicheskiy i estestvenno-nauchnoy podgotovki v inzhenernom obrazovanii. Sbornik trudov IV Mezhdunarodnoy nauchno-metodicheskoy konferentsii [Problems of mathematical and natural science training in engineering education. Proceedings of the IV International Scientific and Methodological Conference]. St. Petersburg, 2017, pp. 135-147.
10. Khodakovskiy V.A., Khodakovskiy T.V. Mera skhodstva uzkopolosnykh signalov. Avtomatika na transporte. PGUPS [A measure of the similarity of narrowband signals. Transport automation. PGUPS]. St. Petersburg, 2015, V.1, I. 2, pp. 180-194.
11. Khodakovskiy V.A., Khodakovskiy T.V. Sintez mnogopolosnogo fil'tra s trebuemoy chastotnoy kharakteristikoy. Intellektual'nye tekhnologii na transporte. [Synthesis of a multi-band filter with the required frequency response. Intelligent technologies in transport]. PGUPS Imperatora Aleksandra I [PGUPS Emperor Alexander I]. St. Petersburg, 2015, I. 1(1), pp. 38-42.
12. Kul'tin V.B., Sukhanov S.A., Khodakovskiy V.A. Polosovoy tsifrovoy fil'tr s vremennoy obrabotkoy v apparature tonal'nykh rel'sovykh tsepey. [Band-pass digital filter with time processing in the equipment of voice-frequency rail circuits]. Avtomatika i telemekhanika zheleznykh dorog Rossii. Novaya tekhnika i novye tekhnologii, sbornik nauchnykh trudov. Peterburgskiy gosudarstvennyy universitet putey soobshcheniya Imperatora Aleksandra I [Automation and telemechanics of Russian railways. New technique and new technologies, collection of scientific papers. Petersburg State University of Communications of Emperor Alexander I]. St. Petersburg, 2007, pp. 94-97.
13. Shamanov V.I. Problemy elektromagnitnoy sovmestimosti rel'sovykh tsepey s tyagovoy set'yu [Problems of electromagnetic compatibility of rail circuits with a traction network]. Moscow: Sistemy upravleniya na transporte Publ. V. 5, I. 2, 2019, pp. 160-185.
14. GOST 33436.2- 2016 Mezhgosudarstvennyy standart. Sovmestimost' tekhnicheskikh sredstv elektromagnitnaya. Sistemy i oborudovanie zheleznodorozhnogo transporta [GOST 33436.2-2016 Interstate standard. Compatibility of technical means is electromagnetic. Systems and equipment of railway transport].
15. Shatokhin V.A. Elektromagnitnaya sovmestimost' sistem zheleznodorozhnoy avtomatiki i telemekhaniki [Electromagnetic compatibility of railway automation and telemechanics systems]. Moscow: Tekhnologii elektromagnitnoy sovmestimosti Publ., I. 1(8), 2004, pp. 22 – 29.
