Frequency-chirprate reassignment

Abstract In this paper, we consider a three-dimensional parameter space, which is the time-frequency-chirprate (TFCR), to characterize the time-varying features of multi-component non-stationary signals. By performing reassignment on the frequency-chirprate plane, a highly concentrated TFCR representation, named as the frequency-chirprate reassignment method (FCRM), is proposed. FCRM can provide the instantaneous frequency (IF) and chirprate (CR) estimates jointly, making the crossing of IFs appear as separated in the TFCR domain, which overcomes the limitation of the popular time-frequency post-processing methods that require input signal with non-overlapping IFs. Based on the chirplet transform, we derive the reassignment center of the FCRM, and a three-dimension ridge detection algorithm is introduced to extract the IFs and CRs from the FCRM. Numerical experiments demonstrate that the proposed FCRM provides a concentrated TFCR representation, obtaining a good IF estimation for the overlapped multi-component signals that contain cross-over IFs.

[1]  Fulei Chu,et al.  Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples , 2013 .

[2]  Chuan Li,et al.  A generalized synchrosqueezing transform for enhancing signal time-frequency representation , 2012, Signal Process..

[3]  Guoan Bi,et al.  IF estimation of FM signals based on time-frequency image , 2015, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Igor Djurovic,et al.  QML-RANSAC Instantaneous Frequency Estimator for Overlapping Multicomponent Signals in the Time-Frequency Plane , 2018, IEEE Signal Processing Letters.

[5]  Sylvain Meignen,et al.  Synchrosqueezing transforms: From low- to high-frequency modulations and perspectives , 2019, Comptes Rendus Physique.

[6]  Igor Djurovic,et al.  A Modified Viterbi Algorithm-Based IF Estimation Algorithm for Adaptive Directional Time–Frequency Distributions , 2018, Circuits Syst. Signal Process..

[7]  Lexing Ying,et al.  Synchrosqueezed Curvelet Transform for Two-Dimensional Mode Decomposition , 2014, SIAM J. Math. Anal..

[8]  Yuanyuan Li,et al.  Sparse Time-Frequency-Frequency-Rate Representation for Multicomponent Nonstationary Signal Analysis , 2018, 2018 26th European Signal Processing Conference (EUSIPCO).

[9]  Kelly Fitz,et al.  Correction to: 'On the Use of Time/Frequency Reassignment in Additive Sound Modeling' , 2002 .

[10]  Douglas L. Jones,et al.  An adaptive optimal-kernel time-frequency representation , 1995, IEEE Trans. Signal Process..

[11]  Benjamin Friedlander,et al.  Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals , 1996, IEEE Trans. Inf. Theory.

[12]  Shibin Wang,et al.  Time-reassigned synchrosqueezing transform: The algorithm and its applications in mechanical signal processing , 2019, Mechanical Systems and Signal Processing.

[13]  K. Kodera,et al.  Analysis of time-varying signals with small BT values , 1978 .

[14]  Vittoria Bruni,et al.  A Fast and Robust Spectrogram Reassignment Method , 2019, Mathematics.

[15]  Lexing Ying,et al.  Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition , 2013, SIAM J. Imaging Sci..

[16]  Ljubisa Stankovic,et al.  Synchrosqueezing-based time-frequency analysis of multivariate data , 2015, Signal Process..

[17]  Maria Sandsten,et al.  Parameter estimation of Oscillating Gaussian functions using the scaled reassigned spectrogram , 2018, Signal Process..

[18]  Vittoria Bruni,et al.  An iterative approach for spectrogram reassignment of frequency modulated multicomponent signals , 2020, Math. Comput. Simul..

[19]  Gang Yu,et al.  General linear chirplet transform , 2016 .

[20]  Sylvain Meignen,et al.  On Demodulation, Ridge Detection, and Synchrosqueezing for Multicomponent Signals , 2017, IEEE Transactions on Signal Processing.

[21]  Xiangxiang Zhu,et al.  Synchroextracting chirplet transform for accurate IF estimate and perfect signal reconstruction , 2019, Digit. Signal Process..

[22]  Jinghuai Gao,et al.  A Time-Synchroextracting Transform for the Time–Frequency Analysis of Seismic Data , 2020, IEEE Geoscience and Remote Sensing Letters.

[23]  D. Looney,et al.  Time-Frequency Analysis of EEG Asymmetry Using Bivariate Empirical Mode Decomposition , 2011, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[24]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[25]  Nabeel Ali Khan,et al.  A highly adaptive directional time–frequency distribution , 2016, Signal Image Video Process..

[26]  Khaled H. Hamed,et al.  Time-frequency analysis , 2003 .

[27]  Vahid Abolghasemi,et al.  Locally Optimized Adaptive Directional Time–Frequency Distributions , 2018, Circuits Syst. Signal Process..

[28]  P. O'Shea.  A new technique for instantaneous frequency rate estimation , 2002, IEEE Signal Processing Letters.

[29]  Vittoria Bruni,et al.  On the time-frequency reassignment of interfering modes in multicomponent FM signals , 2018, 2018 26th European Signal Processing Conference (EUSIPCO).

[30]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[31]  Richard Kronland-Martinet,et al.  Characterization of acoustic signals through continuous linear time-frequency representations , 1996, Proc. IEEE.

[32]  Qian Wang,et al.  Self-Adaptive Generalized S-Transform and Its Application in Seismic Time–Frequency Analysis , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Igor Djurovic,et al.  Cubic phase function: A simple solution to polynomial phase signal analysis , 2017, Signal Process..

[34]  Hau-Tieng Wu,et al.  The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications , 2011, Signal Process..

[35]  Ljubisa Stankovic,et al.  Time-frequency decomposition of multivariate multicomponent signals , 2018, Signal Process..

[36]  Hau-Tieng Wu,et al.  Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples , 2010, SIAM J. Math. Anal..

[37]  Xiang-Gen Xia,et al.  Discrete chirp-Fourier transform and its application to chirp rate estimation , 2000, IEEE Trans. Signal Process..

[38]  Sylvain Meignen,et al.  Time-Frequency Reassignment and Synchrosqueezing: An Overview , 2013, IEEE Signal Processing Magazine.

[39]  Yi Wang,et al.  ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[40]  Gang Yu,et al.  Synchroextracting Transform , 2017, IEEE Transactions on Industrial Electronics.

[41]  Haizhao Yang.  Statistical analysis of synchrosqueezed transforms , 2014, Applied and Computational Harmonic Analysis.

[42]  Ingrid Daubechies,et al.  A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models , 2017 .

[43]  Xiangxiang Zhu,et al.  Multiple squeezes from adaptive chirplet transform , 2019, Signal Process..

[44]  Shibin Wang,et al.  Matching synchrosqueezing transform: A useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis , 2018 .

[45]  Gaigai Cai,et al.  Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis , 2014, IEEE Transactions on Signal Processing.

[46]  Sylvain Meignen,et al.  Chirp Rate and Instantaneous Frequency Estimation: Application to Recursive Vertical Synchrosqueezing , 2017, IEEE Signal Processing Letters.

[47]  Yimin Zhang,et al.  Detection of weak astronomical signals with frequency-hopping interference suppression , 2018, Digit. Signal Process..

[48]  T. Claasen,et al.  THE WIGNER DISTRIBUTION - A TOOL FOR TIME-FREQUENCY SIGNAL ANALYSIS , 1980 .

[49]  Yoonseob Lim,et al.  An Approach to Time-Frequency Analysis With Ridges of the Continuous Chirplet Transform , 2015, IEEE Transactions on Signal Processing.

[50]  Simon Haykin,et al.  The chirplet transform: physical considerations , 1995, IEEE Trans. Signal Process..

[51]  Guang Meng,et al.  Separation of Overlapped Non-Stationary Signals by Ridge Path Regrouping and Intrinsic Chirp Component Decomposition , 2017, IEEE Sensors Journal.

[52]  Po Li,et al.  IF Estimation of Overlapped Multicomponent Signals Based on Viterbi Algorithm , 2020, Circuits Syst. Signal Process..

[53]  Tianyou Liu,et al.  Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution , 2009 .

[54]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[55]  M. Portnoff.  Time-frequency representation of digital signals and systems based on short-time Fourier analysis , 1980 .

[56]  Jianzhong Zhang,et al.  Synchrosqueezing S-Transform and Its Application in Seismic Spectral Decomposition , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[57]  Sylvain Meignen,et al.  Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations , 2015, IEEE Transactions on Signal Processing.

[58]  Haizhao Yang,et al.  Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions , 2013, 1311.4655.

[59]  Sylvain Meignen,et al.  High-Order Synchrosqueezing Transform for Multicomponent Signals Analysis—With an Application to Gravitational-Wave Signal , 2017, IEEE Transactions on Signal Processing.

[60]  I. Daubechies,et al.  Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool , 2011 .

[61]  Jinghuai Gao,et al.  Generalized Ridge Reconstruction Approaches Toward more Accurate Signal Estimate , 2020, Circuits Syst. Signal Process..

[62]  Emmanuel J. Candes,et al.  Detecting highly oscillatory signals by chirplet path pursuit , 2006, gr-qc/0604017.