Approximating the Time-Frequency Representation of Biosignals with Chirplets

A new member of the Cohen's class time-frequency distribution is proposed. The kernel function is determined adaptively based on the signal of interest. The kernel preserves the chirp-like components while removing interference terms generated due to the quadratic characteristic of Wigner-Ville distribution. This approach is based on the chirplet as an underlying model of biomedical signals. We illustrate the method using a number of common biological signals including echo-location and evoked potential signals. Finally, the results are compared with other techniques including chirplet decomposition via matching pursuit and the Choi-Williams distribution function.

[1]  B. Boashash,et al.  Preprocessing and time-frequency analysis of newborn EEG seizures , 2001, IEEE Engineering in Medicine and Biology Magazine.

[2]  M. Born,et al.  Zur Quantenmechanik , 1925 .

[3]  Xiapu Luo,et al.  Ocean clutter suppression using one-class SVM , 2004, Proceedings of the 2004 14th IEEE Signal Processing Society Workshop Machine Learning for Signal Processing, 2004..

[4]  Claire Médigue,et al.  Instantaneous parameter estimation in cardiovascular time series by harmonic and time-frequency analysis , 2002, IEEE Transactions on Biomedical Engineering.

[5]  Antonia Papandreou-Suppappola,et al.  Distributions for time-frequency analysis: a generalization of Choi-Williams and the Butterworth distribution , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[6]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[7]  P. Duvaut,et al.  Window length selection for smoothing the Wigner distribution by applying an adaptive filter technique , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[8]  Dennis Gabor,et al.  Theory of communication , 1946 .

[9]  Ralph D. Hippenstiel,et al.  Time-varying spectral estimation using the instantaneous power spectrum (IPS) , 1990, IEEE Trans. Acoust. Speech Signal Process..

[10]  Patrick Flandrin,et al.  Time-frequency localization from sparsity constraints , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

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

[12]  L. Cohen Generalized Phase-Space Distribution Functions , 1966 .

[13]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[14]  Hideki Kawahara,et al.  YIN, a fundamental frequency estimator for speech and music. , 2002, The Journal of the Acoustical Society of America.

[15]  L.F. Chaparro,et al.  An iterative method for instantaneous frequency estimation , 2001, ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.01EX483).

[16]  Syed Ismail Shah,et al.  Techniques to Obtain Good Resolution and Concentrated Time-Frequency Distributions: A Review , 2009, EURASIP J. Adv. Signal Process..

[17]  J.B. Allen,et al.  A unified approach to short-time Fourier analysis and synthesis , 1977, Proceedings of the IEEE.

[18]  H. Margenau,et al.  Correlation between Measurements in Quantum Theory , 1961 .

[19]  Mostefa Mesbah,et al.  A Nonstationary Model of Newborn EEG , 2007, IEEE Transactions on Biomedical Engineering.

[20]  P. Despland,et al.  The matching pursuit: a new method of characterizing microembolic signals? , 2000, Ultrasound in medicine & biology.

[21]  M. Wickerhauser,et al.  Wavelets and time-frequency analysis , 1996, Proc. IEEE.

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

[23]  Vladimir Shusterman,et al.  Orthonormal-basis partitioning and time-frequency representation of cardiac rhythm dynamics , 2005, IEEE Transactions on Biomedical Engineering.

[24]  Bin He,et al.  Classifying EEG-based motor imagery tasks by means of time–frequency synthesized spatial patterns , 2004, Clinical Neurophysiology.

[25]  Jechang Jeong,et al.  Kernel design for reduced interference distributions , 1992, IEEE Trans. Signal Process..

[26]  Fumikazu Miwakeichi,et al.  Decomposing EEG data into space–time–frequency components using Parallel Factor Analysis , 2004, NeuroImage.

[27]  William J. Williams,et al.  Improved time-frequency representation of multicomponent signals using exponential kernels , 1989, IEEE Trans. Acoust. Speech Signal Process..

[28]  J. Saniie,et al.  A successive parameter estimation algorithm for chirplet signal decomposition , 2006, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[29]  P. Flandrin,et al.  A general class of estimators for the wigner-ville spectrum of non-stationary processes , 1984 .

[30]  Sheng-Min Huang,et al.  Instantaneous frequency-based ultrasonic temperature estimation during focused ultrasound thermal therapy. , 2009, Ultrasound in medicine & biology.

[31]  Cornel Ioana,et al.  On the use of time-frequency warping operators for analysis of marine-mammal signals , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[32]  P. Bertrand,et al.  Optimum smoothing of the Wigner-Ville distribution , 1987, IEEE Trans. Acoust. Speech Signal Process..

[33]  R. Quian Quiroga,et al.  Single-trial event-related potentials with wavelet denoising , 2003, Clinical Neurophysiology.

[34]  J. Saniie,et al.  Chirplet transform for ultrasonic signal analysis and nde applications , 2005, IEEE Ultrasonics Symposium, 2005..

[35]  Patrick Flandrin,et al.  Wigner-Ville spectral analysis of nonstationary processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[36]  Willy Wong,et al.  The adaptive chirplet transform and visual evoked potentials , 2006, IEEE Transactions on Biomedical Engineering.

[37]  Gerald Matz,et al.  Time-Frequency ARMA Models and Parameter Estimators for Underspread Nonstationary Random Processes , 2007, IEEE Transactions on Signal Processing.

[38]  Andrew K. Chan,et al.  Linear frequency-modulated signal detection using Radon-ambiguity transform , 1998, IEEE Trans. Signal Process..

[39]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[40]  Stphane Mallat,et al.  A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way , 2008 .

[41]  Dario Farina,et al.  Time–frequency analysis and estimation of muscle fiber conduction velocity from surface EMG signals during explosive dynamic contractions , 2005, Journal of Neuroscience Methods.

[42]  Seung Ho Doo,et al.  Fast time-frequency domain reflectometry based on the AR coefficient estimation of a chirp signal , 2009, 2009 American Control Conference.

[43]  S. Mallat A wavelet tour of signal processing , 1998 .

[44]  Paolo Bonato,et al.  Time-frequency parameters of the surface myoelectric signal for assessing muscle fatigue during cyclic dynamic contractions , 2001, IEEE Transactions on Biomedical Engineering.

[45]  Ning Ma,et al.  Time-frequency representation of multicomponent chirp signals , 1997, Signal Process..

[46]  Douglas L. Jones,et al.  An adaptive optimal-kernel time-frequency representation , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[47]  Micah M. Murray,et al.  Adaptive tracking of EEG oscillations , 2010, Journal of Neuroscience Methods.

[48]  L. Cohen Distributions concentrated along the instantaneous frequency , 1990 .

[49]  Syed Ismail Shah,et al.  Computing Deblurred Time-Frequency Distributions Using Artificial Neural Networks , 2008 .