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9
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vol 63 / September, 2020
Article

DOI 10.17586/0021-3454-2020-63-3-206-212

UDC 621.396:681.323

Harmonic Oscillation Spectrum under Frequency Modulation by a Random Signal

S. I. Ziatdinov
St. Petersburg State University of Aerospace Instrumentation, Department of Information Network Technologies; Professor


L. A. Osipov
St. Petersburg State University of Aerospace Instrumentation, Department of Information Network Technologies; Professor


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Abstract. The frequency properties of a signal modulated by a random process with a nonzero average frequency are investigated. It is shown that the energy spectrum of frequency-modulated harmonic oscillation is infinitely wide and contains a discrete spectral line and a partial region at the frequency of the modulated oscillation, as well as partial regions corresponding to the harmonics of the middle frequency of the modulating narrow-band random signal relative to the modulated oscillation frequency. The spectral regions width depends on the variance and number of the corresponding harmonic of the average frequency of the modulating signal. Results of calculations of the energy spectrum of frequency-modulated harmonic oscillations are presented. It is noted that derived relations for the correlation function and the energy spectrum of the frequency-modulated signal can be used in study and development of information transmission systems with angular modulation of the carrier wave.
Keywords: frequency modulation, random signal, correlation function, energy spectrum

References:

 

  1. Middleton D. An introduction to statistical communication theory, NY, McGraw-Hill, 1960.
  2. Tikhonov V.I. Statisticheskaya radiotekhnika (Statistical Radio Engineering), Moscow, 1966, 678 р. (in Russ.)
  3. Levin B.R. Teoreticheskiye osnovy statisticheskoy radiotekhniki (Theoretical Foundations of Statistical Radio Engineering), Moscow, 1969, 751 р. (in Russ.)
  4. Tikhonov V.I. Statisticheskiy analiz i sintez radiotekhnicheskikh ustroystv i sistem (Statistical Analysis and Synthesis of Radio Engineering Devices and Systems), Moscow, 1991, 608 р. (in Russ.)
  5. Tikhonov V.I., Kharisov V.N. Statisticheskiy analiz i sintez radiotekhnicheskikh ustroystv i sistem (Statistical Analysis and Synthesis of Radio Engineering Devices and Systems), Moscow, 2004, 608 р. (in Russ.)
  6. Goryainov V.T., Zhuravlev A.G., Tikhonov V.I. Statisticheskaya radiotekhnika. Primery i zadachi (Statistical Radio Engineering. Examples and Tasks), Moscow, 1980, 543 р. (in Russ.)
  7. Goryainov V.T. Statisticheskaya radiotekhnika. Primery i zadachi po statisticheskoy radiotekhnike (Statistical Radio Engineering. Examples and Tasks in Statistical Radio Engineering), Moscow, 1979, 597 р. (in Russ.)
  8. Rove H. Proc. IEEE, 1964, no. 4.
  9. Shakhtinskiy B.I. Sluchaynyye protsessy v radiotekhnike (Random Processes in Radio Engineering), Moscow, 2000,583 р. (in Russ.)
  10. Gonorovskiy I.S. Radiotekhnicheskie tsepi i signaly (Radio Engineering Chains and Signals), Moscow, 1986, 512 p. (in Russ.)
  11. Baskakov S.I. Radiotekhnicheskiye tsepi i signaly (Radio Circuits and Signals), Moscow, 2016, 915 р. (in Russ.)
  12. Moshchenskiy Yu.V., Nechayev A.S. Teoreticheskiye osnovy radiotekhniki (Theoretical Foundations of Radio Engineering), St. Petersburg, 2018, 147 р. (in Russ.)
  13. Piskunov N.S. Differentsial'noye i integral'noye ischisleniya (Differential and Integral Calculus), Moscow, 1965, vol. 2, 312 р. (in Russ.)
  14. Shakhmeyster A.Kh. Trigonometriya (Trigonometry), Moscow, 2013, 752 р. (in Russ.)