Advertisement

Output Frequency Characteristics of Nonlinear Systems

  • Xingjian Jing
  • Ziqiang Lang
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Some interesting properties of output frequencies of Volterra-type nonlinear systems are particularly investigated. These results provide a very novel and useful insight into the super-harmonic and inter-modulation phenomena in output frequency response of nonlinear systems, with consideration of the effects incurred by different nonlinear components in the system. The new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction (or coupling effects) between different harmonic behaviors in system output frequency response incurred by different nonlinear components. These results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities. They can provide an important guidance to modeling, identification, control and signal processing by using the Volterra series theory in practice.

References

  1. Bedrosian E, Rice SO (1971) The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs. Proc IEEE 59:1688CrossRefMathSciNetGoogle Scholar
  2. Billings SA, Lang ZQ (2002) Nonlinear systems in the frequency domain: energy transfer filters. Int J Control 75(14):1066–1081CrossRefMATHMathSciNetGoogle Scholar
  3. Bussgang JJ, Ehrman L, Graham JW (1974) Analysis of nonlinear systems with multiple inputs. Proc IEEE 62(8):1088–1119CrossRefGoogle Scholar
  4. Frank WA (1996) Sampling requirements for Volterra system identification. IEEE Signal Process Lett 3(9):266–268CrossRefGoogle Scholar
  5. Jing XJ, Lang ZQ, Billings SA, Tomlinson GR (2006) The parametric characteristic of frequency response functions for nonlinear systems. Int J Control 79(12):1552–1564CrossRefMATHMathSciNetGoogle Scholar
  6. Jing XJ, Lang ZQ, Billings SA (2008a) Frequency domain analysis for suppression of output vibration from periodic disturbance using nonlinearities. J Sound Vib 314:536–557CrossRefGoogle Scholar
  7. Jing XJ, Lang ZQ, Billings SA (2010) Output frequency properties of nonlinear systems. Int J Nonlinear Mech 45(7):681–690CrossRefGoogle Scholar
  8. Lang ZQ, Billings SA (1996) Output frequency characteristics of nonlinear systems. Int J Control 64:1049–1067CrossRefMATHMathSciNetGoogle Scholar
  9. Lang ZQ, Billings SA (1997) Output frequencies of nonlinear systems. Int J Control 57(5):713–730CrossRefMathSciNetGoogle Scholar
  10. Lang ZQ, Billings SA (2000) Evaluation of output frequency responses of nonlinear systems under multiple inputs. IEEE Trans Circuits Syst II Analog Digital Signal Process 47(1):28–38CrossRefMATHGoogle Scholar
  11. Raz GM, Van Veen BD (1998) Baseband Volterra filters for implementing carrier based nonlinearities. IEEE Trans Signal Process 46(1):103–114CrossRefGoogle Scholar
  12. Wei H-L, Lang Z-Q, Billings SA (2007) An algorithm for determining the output frequency range of Volterra models with multiple inputs. IEEE Trans Circuits Syst II Express Brief 54(6):532–536CrossRefGoogle Scholar
  13. Wu XF, Lang ZQ, Billings SA (2007) Analysis of the output frequencies of nonlinear systems. IEEE Trans Signal Process 55(7):3239–3246CrossRefMathSciNetGoogle Scholar
  14. Yuan F, Opal A (2001) Distortion analysis of periodically switched nonlinear circuits using time-varying Volterra series. IEEE Trans Circuits Syst I Fund Theory Appl 48(6):726–738CrossRefMATHMathSciNetGoogle Scholar
  15. Zhou L, Misawa EA (2005) Low frequency vibration suppression shape filter and high frequency vibration suppression shape filter. In: American control conference, Portland, OR, 8–10 June 2005, pp 4742–4747Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Xingjian Jing
    • 1
  • Ziqiang Lang
    • 2
  1. 1.The Hong Kong Polytechnic UniversityHong KongPR China
  2. 2.The University of SheffieldSheffieldUK

Personalised recommendations