Parametric Time-frequency Modeling of Nonstationary Signals by Adaptive Decomposition Based on Time-shearing Gabor Atoms

2007 ◽  
pp. 203-207
Author(s):  
Shiwei Ma ◽  
Zhongjie Liu ◽  
Weibin Liang
Keyword(s):  
Nonstationary Signals ◽  
Time Frequency ◽  
Adaptive Decomposition

RECENT MATHEMATICAL DEVELOPMENTS ON EMPIRICAL MODE DECOMPOSITION

2009 ◽  
Vol 01 (04) ◽  
pp. 681-702 ◽  
Author(s):  
YUESHENG XU ◽  
HAIZHANG ZHANG
Keyword(s):  
Empirical Mode Decomposition ◽  
Piecewise Linear ◽  
Basis Functions ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Bedrosian Identity ◽  
Adaptive Data Analysis ◽  
Adaptive Decomposition ◽  
Two Stages

Building the mathematical foundation for the empirical mode decomposition is an important issue in adaptive data analysis. The task of building such a foundation consists of two stages. The first is to construct a large bank of basis functions for the time–frequency analysis of nonlinear and nonstationary signals. The second is to establish a fast adaptive decomposition algorithm. We survey recent mathematical progress on these two stages. Related results on piecewise linear spectral sequences and the Bedrosian identity are also reviewed.

scholarly journals A combined generalized Warblet transform and second order synchroextracting transform for analyzing nonstationary signals of rotating machinery

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kai Wei ◽  
Xuwen Jing ◽  
Bingqiang Li ◽  
Chao Kang ◽  
Zhenhuan Dou ◽  
...  
Keyword(s):  
Vibration Signal ◽  
Rotating Machinery ◽  
Second Order ◽  
Variable Speed ◽  
Short Time Fourier Transform ◽  
Stationary Characteristic ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Effective Technology ◽  
Short Time

AbstractIn recent years, considerable attention has been paid in time–frequency analysis (TFA) methods, which is an effective technology in processing the vibration signal of rotating machinery. However, TFA techniques are not sufficient to handle signals having a strong non-stationary characteristic. To overcome this drawback, taking short-time Fourier transform as a link, a TFA methods that using the generalized Warblet transform (GWT) in combination with the second order synchroextracting transform (SSET) is proposed in this study. Firstly, based on the GWT and SSET theories, this paper proposes a method combining the two TFA methods to improve the TFA concentration, named GWT–SSET. Secondly, the method is verified numerically with single-component and multi-component signals, respectively. Quantized indicators, Rényi entropy and mean relative error (MRE) are used to analyze the concentration of TFA and accuracy of instantly frequency (IF) estimation, respectively. Finally, the proposed method is applied to analyze nonstationary signals in variable speed. The numerical and experimental results illustrate the effectiveness of the GWT–SSET method.

High-concentration time–frequency analysis for multi-component nonstationary signals based on combined multi-window Gabor transform

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qiang Wang ◽  
Chen Meng ◽  
Cheng Wang
Keyword(s):  
Optimal Solution ◽  
Iteration Process ◽  
Perfect Reconstruction ◽  
Gabor Transform ◽  
Zak Transform ◽  
High Concentration ◽  
Content Type ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Optimization Function

PurposeThis study aims to reveal the essential characteristics of nonstationary signals and explore the high-concentration representation in the joint time–frequency (TF) plane.Design/methodology/approachIn this paper, the authors consider the effective TF analysis for nonstationary signals consisting of multiple components.FindingsTo make it, the authors propose the combined multi-window Gabor transform (CMGT) under the scheme of multi-window Gabor transform by introducing the combination operator. The authors establish the completeness utilizing the discrete piecewise Zak transform and provide the perfect-reconstruction conditions with respect to combined TF coefficients. The high-concentration is achieved by optimization. The authors establish the optimization function with considerations of TF concentration and computational complexity. Based on Bergman formulation, the iteration process is further analyzed to obtain the optimal solution.Originality/valueWith numerical experiments, it is verified that the proposed CMGT performs better in TF analysis for multi-component nonstationary signals.

Research and Comparison of Time-frequency Techniques for Nonstationary Signals

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
Qiang Zhu ◽  
Yansong Wang ◽  
Gongqi Shen
Keyword(s):  
Nonstationary Signals ◽  
Time Frequency

scholarly journals A software companion for compressively sensed time–frequency processing of sparse nonstationary signals

SoftwareX ◽  
2018 ◽  
Vol 8 ◽  
pp. 9-10 ◽  
Author(s):  
Ervin Sejdić ◽  
Irena Orović ◽  
Srdjan Stanković
Keyword(s):  
Nonstationary Signals ◽  
Time Frequency ◽  
Frequency Processing
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