Generalized Ridge Reconstruction Approaches Toward more Accurate Signal Estimate

  • Xiangxiang Zhu
  • Zhuosheng ZhangEmail author
  • Hanqiu Zhang
  • Jinghuai Gao
  • Bei Li


Ridge reconstruction (RR) method is one of the most commonly used ways for multicomponent signal reconstruction from time–frequency representations. However, this method leads to large reconstruction error when dealing with strongly amplitude-modulated and frequency-modulated (AM–FM) signals. In this paper, we first give the error analysis of RR method based on short-time Fourier transform when the amplitude and frequency modulations are not negligible. Then, two generalized ridge reconstruction approaches are proposed to overcome the limitations existing in the standard RR method. The first approach relies on a second-order local expansion of phase function, and the chirp rate is employed to improve the reconstruction. The second one is supported by the fact that RR is exact for pure sinusoidal signals; thus, demodulation operator is performed to facilitate the ridge reconstruction. A simple theoretical analysis of the proposed two approaches is provided. Numerical experiments on simulated and real signals demonstrate that the proposed approaches can obtain a more accurate signal estimate for strongly FM signals, being stable for the selection of window length and keeping a good noise robustness.


Multicomponent signal decomposition Ridge reconstruction Time–frequency representation Demodulation FM signals 



This work is supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91730306) and National Key R and D Program of the Ministry of Science and Technology of China with the Project Integration Platform Construction for Joint Inversion and Interpretation of Integrated Geophysics (Grant No. 2018YFC0603501). X. Zhu thanks the China Scholarship Council for their support. The authors thank the anonymous reviewers for their valuable comments and suggestions that improve the quality of this paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Xiangxiang Zhu
    • 1
  • Zhuosheng Zhang
    • 1
    Email author
  • Hanqiu Zhang
    • 2
  • Jinghuai Gao
    • 3
  • Bei Li
    • 1
  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  2. 2.Melbourne School of EngineeringThe University of MelbourneVictoriaAustralia
  3. 3.National Engineering Laboratory for Offshore Oil ExplorationXi’anChina

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