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