Russian Journal of Nondestructive Testing

, Volume 54, Issue 1, pp 44–54 | Cite as

Instantaneous Frequency Estimation for Motion Echo Signal of Projectile in Bore Based on Polynomial Chirplet Transform

  • Jian Wang
  • Yan Han
  • Li Ming Wang
  • Pi Zhuang Zhang
  • Ping Chen
Acoustic Methods


Microwave interferometer is one of the devices for measuring the movement travel–varying or time-varying velocity of projectile in bore. Microwave interferometer first obtains the Doppler echo signal including the motion information of the projectile in bore, then the velocity is measured based on instantaneous frequency estimation (IFE) of the processed and transformed signal. The parametric time-frequency analysis method can make spectral energy of nonlinear frequency modulation (FM) signal concentrate at some range in the new transform domain. As the motion echo signal of projectile in bore (MSPB) is a nonlinear FM signal, it could be described by polynomial chirplet, one of polynomial FM signal modes, which is used to construct transform kernel for the signal. In this paper, Polynomial chirplet transform (PCT) method is proposed to analyze the simulation and experiment echo signals of projectile in bore. The estimation error and Renyi entropy are used to measure quantify of the time-frequency distribution. Compared with short-time Fourier transform (STFT) method and Wigner-Ville distribution (WVD) method, our results show that the PCT method has most powerful anti-interference performance and highest accuracy of instantaneous frequency estimation for the simulation signal, and lowest Renyi entropy of the instantaneous frequency estimation for the experiment signal. In general, the PCT method has powerful anti-interference performance and high time-frequency concentration and accuracy of instantaneous frequency estimation for the motion echo signal of projectile in bore.


time-frequency concentration instantaneous frequency estimation polynomial chirplet transform parametric time-frequency analysis 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Jian Wang
    • 1
    • 2
  • Yan Han
    • 1
    • 2
  • Li Ming Wang
    • 1
    • 2
  • Pi Zhuang Zhang
    • 1
    • 2
  • Ping Chen
    • 1
    • 2
  1. 1.Key Laboratory of Information Detection and ProcessingNorth University of ChinaTaiyuan ShanxiChina
  2. 2.School of Information and Communication EngineeringNorth University of ChinaTaiyuan, ShanxiChina

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