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A refined formula for the autocorrelation function of an M-sequence

  • Stochastic Systems, Queueing Systems
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Abstract

We consider a widespread impreciseness in the autocorrelation function formula for M-sequences. We propose a derivation of the exact expression for the normalized autocorrelation function for a p-ary sequence in almost all points of the temporal argument inside a period. We justify the value balance property for the periodic autocorrelation function that lets us obtain analytic expressions for peak outliers of the autocorrelation inside a minimal period for ternary and quinary M-sequences.

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References

  1. Ipatov, V., Shirokopolosnye sistemy i kodovoe razdelenie signalov. Printsipy i prilozheniya (Wideband Systems and Coding Signal Separation. Principles and Applications), Moscow: Tekhnosfera, 2007.

    Google Scholar 

  2. Gill, A., Linear Sequential Circuits; Analysis, Synthesis, and Applications, New York: McGraw-Hill, 1966. Translated under the title Lineinye posledovatel’hostnye mashiny, Moscow: Nauka, 1974.

    MATH  Google Scholar 

  3. Kir’yanov, B.F., The Microcomputer as a Means for Imitation and Processing of Random Processesin Radiotechnical Systems, Novgorod: Novgorod. Polytekhn. Inst., 1986, Available from VINITI, 1986, no. 7646-V86.

    Google Scholar 

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Authors and Affiliations

  1. Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, Russia

    B. F. Kir’yanov

  2. Kazan National Research Technological University, Kazan, Russia

    V. M. Kuznetsov & V. A. Pesoshin

Authors
  1. B. F. Kir’yanov
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  2. V. M. Kuznetsov
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  3. V. A. Pesoshin
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Corresponding author

Correspondence to B. F. Kir’yanov.

Additional information

Original Russian Text © B.F. Kir’yanov, V.M. Kuznetsov, V.A. Pesoshin, 2015, published in Avtomatika i Telemekhanika, 2015, No. 7, pp. 101–110.

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Kir’yanov, B.F., Kuznetsov, V.M. & Pesoshin, V.A. A refined formula for the autocorrelation function of an M-sequence. Autom Remote Control 76, 1221–1228 (2015). https://doi.org/10.1134/S0005117915070073

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  • DOI: https://doi.org/10.1134/S0005117915070073

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