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

## Abstract

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.

## Keywords

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

### Acknowledgments

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).

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