# The Analysis of Periodic Signal Detection Method Based on Duffing System Chaotic Dynamics

## DOI:

https://doi.org/10.20535/RADAP.2018.74.5-10## Keywords:

weak signal detection, chaotic systems, signal-to-noise ratio, phase portrait## Abstract

This article presents the analysis of periodic signal detection method based on Duffing system sensitivity to weak influences.The described signal detection method is developed with using of Duffing system that oscillates in chaotic state, without transitions to periodic state. The main advantage of such method is the absence of periodic oscillation modes with low sensitivity.

The divergence of Duffing system phase trajectories is investigated with influences of different periodic signals under low signal-to-noise ratio values. The estimation of phase trajectories divergence is performed with using of numeric integration.

The signal detection method is analyzed with different forms of input signal: sinusoidal, square, triangle. The analysis shows that a reliable detection of periodic signal can be performed for any of the three presented forms of signal with repeating frequency near the frequency of the driving signal.

The obtained results show wide capabilities of Duffing system applications for detection of weak periodic signals.

## References

Vaseghi S.V. (2008) *Advanced Digital Signal Processing and Noise Reduction*. DOI: 10.1002/9780470740156

Shannon C. (1949) Communication in the Presence of Noise. *Proceedings of the IRE*, Vol. 37, Iss. 1, pp. 10-21. DOI: 10.1109/jrproc.1949.232969

Kumar A. (2018) Design and simulation of MIMO and massive MIMO for 5G mobile communication system. *International Journal of Wireless and Mobile Computing*, Vol. 14, Iss. 2, pp. 197. DOI: 10.1504/ijwmc.2018.10012260

Kotel'nikov V.A., Silverman R.A. and Turin G.L. (1960) The Theory of Optimum Noise Immunity. *Physics Today*, Vol. 13, Iss. 8, pp. 40-42. DOI: 10.1063/1.3057075

Boiko J. M. (2015) Increasing the noise immunity of signal processing units of telecommunications on the basis of the modified synchronization schemes. *Visn. NTUU KPI, Ser. Radioteh. radioaparatobuduv.*, no. 61, pp. 91-107. DOI: 10.20535/RADAP.2015.61.91-107

Kalinin V.I. and Chapursky V.V. (2008) UWB wireless communications with signal correlation processing. *2008 18th International Crimean Conference - Microwave & Telecommunication Technology*. DOI: 10.1109/crmico.2008.4676380

Shapiro R. (1975) Linear filtering. *Mathematics of Computation*, Vol. 29, Iss. 132, pp. 1094-1094. DOI: 10.1090/s0025-5718-1975-0389356-x

Vetterli M. and Prandoni P. (2008) *Signal Processing for Communications*. DOI: 10.1201/9781439808009

Haykin S., Yee P. and Derbez E. (1997) Optimum nonlinear filtering. *IEEE Transactions on Signal Processing*, Vol. 45, Iss. 11, pp. 2774-2786. DOI: 10.1109/78.650104

Luchinsky D., Mannella R., McClintock P. and Stocks N. (1999) Stochastic resonance in electrical circuits. I. Conventional stochastic resonance. *IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing*, Vol. 46, Iss. 9, pp. 1205-1214. DOI: 10.1109/82.793710

McNamara B. and Wiesenfeld K. (1989) Theory of stochastic resonance. *Physical Review A*, Vol. 39, Iss. 9, pp. 4854-4869. DOI: 10.1103/physreva.39.4854

Casado-Pascual J., Gómez-Ordóñez J., Morillo M. and Hänggi P. (2003) Two-State Theory of Nonlinear Stochastic Resonance. *Physical Review Letters*, Vol. 91, Iss. 21. DOI: 10.1103/physrevlett.91.210601

Markley F.L., Crassidis J. and Cheng Y. (2005) Nonlinear Attitude Filtering Methods. *AIAA Guidance, Navigation, and Control Conference and Exhibit*. DOI: 10.2514/6.2005-5927

Madisetti V. (2009) Digital Signal Processing Fundamentals. *Electrical Engineering Handbook*. DOI: 10.1201/9781420046076

Sivakrishna S. and Yarrabothu R.S. (2018) Design and simulation of 5G massive MIMO kernel algorithm on SIMD vector processor. *2018 Conference on Signal Processing And Communication Engineering Systems (SPACES)*. DOI: 10.1109/spaces.2018.8316315

Jarry P. and Beneat J.N. (2015) Digital Communications. *Digital Communications*, pp. 3-5. DOI: 10.1016/b978-1-78548-037-9.50001-6

Chunyan N. and Zhuwen W. (2011) Application of Chaos in Weak Signal Detection. *2011 Third International Conference on Measuring Technology and Mechatronics Automation*. DOI: 10.1109/icmtma.2011.134

Jung S.N., Longtin A. and Maler L. (2016) Weak signal amplification and detection by higher-order sensory neurons. *Journal of Neurophysiology*, Vol. 115, Iss. 4, pp. 2158-2175. DOI: 10.1152/jn.00811.2015

Gao S.-L., Zhong S.-C., Wei K. and Ma H. (2012) Weak signal detection based on chaos and stochastic resonance. *Acta Phys. Sin*, Vol. 61, Iss. 18, pp. 180501. DOI: 10.7498/aps.61.180501

Lu P. and Li Yu. (2005) A Modified Chaos-Based Weak Sinusoidal Signal Amplitude Detection Approach[J]. *Chinese Journal of Electronics*, Vol. 33, Iss. 3, pp. 527-529.

Wang G., Chen D., Lin J. and Chen X. (1999) The application of chaotic oscillators to weak signal detection. *IEEE Transactions on Industrial Electronics*, Vol. 46, Iss. 2, pp. 440-444. DOI: 10.1109/41.753783

Korneta W., Garcia-Moreno E. and Sena A. (2015) Noise activated dc signal sensor based on chaotic Chua circuit. *Communications in Nonlinear Science and Numerical Simulation*, Vol. 24, Iss. 1-3, pp. 145-152. DOI: 10.1016/j.cnsns.2014.12.010

Rohde G.K., Nichols J.M. and Bucholtz F. (2008) Chaotic signal detection and estimation based on attractor sets: Applications to secure communications. *Chaos: An Interdisciplinary Journal of Nonlinear Science*, Vol. 18, Iss. 1, pp. 013114. DOI: 10.1063/1.2838853

Liu F., Wang J. and Wang W. (1999) Frequency sensitivity in weak signal detection. *Physical Review E*, Vol. 59, Iss. 3, pp. 3453-3460. DOI: 10.1103/physreve.59.3453

Li Y. (2003) Chaotic system for the detection of periodic signals under the background of strong noise. *Chinese Science Bulletin*, Vol. 48, Iss. 5, pp. 508. DOI: 10.1360/03tb9107

Wei C., Chen M., Cheng W. and Zhe Z. (2009) Summary on weak signal detection methods based on Chaos theory. *2009 9th International Conference on Electronic Measurement & Instruments*. DOI: 10.1109/icemi.2009.5274836

Martynyuk, V. V., Fedula, M. V. (2013) Weak periodic signal detection with the fractional order modified Duffing-Holmes system. *Visn. NTUU KPI, Ser. Radioteh. radioaparatobuduv.*, no. 53, pp. 13-22. DOI: 10.20535/RADAP.2013.53.13-22

Sun Wenjun, Rui Guosheng, Zhang Yang and Wang Lin (2013) Chaotic oscillator detection method for weak signals. *Journal of Data Acquisition & Processing*, Vol. 2013-03.

Rongbiao Z., Fuhuan C., Li R. and Jianguang G. (2011) Weak Signal Detection Method under the Strong Noise Background. *Advances in Intelligent and Soft Computing*, pp. 417-425. DOI: 10.1007/978-3-642-25185-6_54

Le B. (2005) Chaotic Oscillator and Other Techniques for Detection of Weak Signals. *IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, Vol. E88-A, Iss. 10, pp. 2699-2701. DOI: 10.1093/ietfec/e88-a.10.2699

Korsch H.J. and Jodl H. (1994) The Duffing Oscillator. *Chaos*, pp. 157-180. DOI: 10.1007/978-3-662-02991-6_8

Martynyuk V., Fedula M. and Balov O. (2014) Periodic Signal Detection with Using Duffing System Poincare Map Analysis. *Adv. Sci. Technol. Res J.*, Vol. 8, Iss. 22, pp. 26–30. DOI: 10.12913/22998624.1105158

## Downloads

## Published

## How to Cite

*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, 0(74), pp. 5-10. doi: 10.20535/RADAP.2018.74.5-10.

## Issue

## Section

## License

Authors who publish with this journal agree to the following terms:

- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).