Dynamic Variance Analysis of One-Dimensional Signal in Gaussian Noise Based on Recursive Formula

  • Lang Yu
  • Wenqing Wu
  • Gang HeEmail author
  • Wenxin Yu
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1084)


Gaussian noise is a statistical noise having a probability density function (PDF) equal to that of the normal distribution (which is also known as the Gaussian distribution). In telecommunications and computer networks, communication channels may be affected by broadband Gaussian noise from many natural sources, such as thermal vibrations of atoms in a conductor (called thermal noise or Johnson-Nyquist noise), shot noise, from Earth and other warm objects, as well as celestial bodies such as the sun. Therefore, Gaussian noise is particularly common in signal communication. It is determined by two parameters, mean and variance. Therefore, when filtering a random signal containing a Gaussian noise, it is necessary to perform variance analysis and mean calculation. As the most commonly used basic statistic, variance describes the distance between the sample data and the sample mean. It is widely used in finance, aerospace, communications and other fields. When calculating the variance of the Gaussian noise with real-time high-speed variation, the traditional definition algorithm adopts the full-sample algorithm, and the algorithm has the disadvantages of inefficiency when dealing with such real-time changing data. Aiming at this problem, this paper proposes a new real-time variance dynamic recursive algorithm based on the sliding window idea, which makes the workload of computer reading data significantly reduced. Finally, through simulation experiments, it is applied to the mean and variance estimation of Gaussian noise with real-time high-speed variation. The experimental results show that the algorithm significantly improves the efficiency of calculating the variance and mean of Gaussian noise. This verifies the correctness and practicability of this algorithm.


Time-varying variance Recursive formula Algorithm complexity Sliding window Gaussian noise 



This paper has been supported by the Doctoral Research Foundation of Southwest University of Science and Technology (No. 16zx7108, No. 15zx7151. No.15zx7118), the Educationa1 Reform Research Project of Southwest University of Science and Technology (No. 15xnzd05) and the Undergraduate Innovation Fund Project Accurate Funding Special Project by Southwest University of Science and Technology (No. JZ19-057).


  1. 1.
    Chen, A.S., Chang, H.C., Cheng, L.Y.: Time-varying variance scaling: application of the fractionally integrated ARMA model. N. Am. J. Econ. Financ. 47, 1–12 (2019)CrossRefGoogle Scholar
  2. 2.
    Chu, A.M.Y., Li, R.W.M., So, M.K.P.: Bayesian spatial–temporal modeling of air pollution data with dynamic variance and leptokurtosis. Spat. Stat. 26, 1–20 (2018)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Yang, Y., Wang, S.: Two simple tests of the trend hypothesis under time-varying variance. Econ. Lett. 156, 123–128 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wang, J., Wang, L., He, X.: The study of high accuracy time keeping based on FPGA when navigation satellite losing connection. Chin. J. Electron Devices 39(01), 140–143 (2016)Google Scholar
  5. 5.
    Liu, J., Sun, X.M.: Real-time calculation method of non-zero mean measurement and control data variance. Math. Res. Study 21, 148–150 (2016)Google Scholar
  6. 6.
    Chen, H.R., Gao, H.: A unified recurrence formula for k-order origin moments of common discrete distributions. J. Hunan Bus. Coll. 02, 110–111 (2002)Google Scholar
  7. 7.
    Deng, H.B., Liu, J.F., Wang, Y.N.: Recursive algorithm of mean variance and its application. Comput. Mod. 04, 9–11 (1996)Google Scholar
  8. 8.
    Chen, Q.B.: Recursive formula of k-order origin moments of discrete distribution. Stat. Inf. Forum 01, 26–28 (2000)Google Scholar
  9. 9.
    Chen, Q.B., Ma, Y.H.: Recursive formula of k-order central moment of discrete distribution. Stat. Inf. Forum 02, 36–38+72 (1999)Google Scholar
  10. 10.
    Chen, C.G.: The counting method of k-order central moment of three kinds of discrete random variable. J. Jianghan Univ. (Nat. Sci.) 06, 66–68 (2000)Google Scholar
  11. 11.
    Fan, S.F.: Recurrence formula calculating the statistics for changed sample size. J. Inn. Mong. Coll. Agric. Anim. Husb. 01, 153–162 (1990)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of ScienceSouthwest University of Science and TechnologyMianyangChina
  2. 2.School of Computer Science and TechnologySouthwest University of Science and TechnologyMianyangChina

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