A Window Width Optimized S-Transform

Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme can provide much improved energy concentration in the time-frequency domain in comparison with the standard S-transform. It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other standard linear techniques, such as short-time Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.

[1]  C. Robert Pinnegar,et al.  Time-frequency and time-time filtering with the S-transform and TT-transform , 2005, Digit. Signal Process..

[2]  Jin Jiang,et al.  Fault diagnosis in machine tools using selective regional correlation , 2006 .

[3]  C. Robert Pinnegar,et al.  The Bi-Gaussian S-Transform , 2002, SIAM J. Sci. Comput..

[4]  R. G. Stockwell,et al.  S-transform analysis of gravity wave activity from a small scale network of airglow imagers , 1999 .

[5]  Igor Djurovic,et al.  A virtual instrument for time-frequency analysis , 1999, IEEE Trans. Instrum. Meas..

[6]  Tzu-Hsien Sang,et al.  Renyi information and signal-dependent optimal kernel design , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  Karlheinz Gröchenig,et al.  Foundations of Time-Frequency Analysis , 2000, Applied and numerical harmonic analysis.

[8]  William J. Williams,et al.  Uncertainty, information, and time-frequency distributions , 1991, Optics & Photonics.

[9]  Georgios B. Giannakis,et al.  Hybrid FM-polynomial phase signal modeling: parameter estimation and Cramer-Rao bounds , 1999, IEEE Trans. Signal Process..

[10]  Stephen Theophanis,et al.  Color display of the localized spectrum , 2000 .

[11]  Douglas L. Jones,et al.  A high resolution data-adaptive time-frequency representation , 1990, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Johann F. Böhme,et al.  Evaluation of knock begin in spark ignition engines by least squares , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[13]  C. Marchesi,et al.  Spectral analysis of cardiovascular time series by the S-transform , 1997, Computers in Cardiology 1997.

[14]  Jin Jiang,et al.  Heart sound analysis using the S transform , 2000, Computers in Cardiology 2000. Vol.27 (Cat. 00CH37163).

[15]  G. Panda,et al.  Power Quality Analysis Using S-Transform , 2002, IEEE Power Engineering Review.

[16]  C. Robert Pinnegar,et al.  The S-transform with windows of arbitrary and varying shape , 2003 .

[17]  Jin Jiang,et al.  Selective Regional Correlation for Pattern Recognition , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[18]  Lalu Mansinha,et al.  Localization of the complex spectrum: the S transform , 1996, IEEE Trans. Signal Process..

[19]  C. Robert Pinnegar,et al.  Time-local Fourier analysis with a scalable, phase-modulated analyzing function: the S-transform with a complex window , 2004, Signal Process..

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

[21]  P. McFadden,et al.  DECOMPOSITION OF GEAR VIBRATION SIGNALS BY THE GENERALISED S TRANSFORM , 1999 .

[22]  Igor Djurovic,et al.  Estimation of multicomponent signals by using time-frequency representations with application to knock signal analysis , 2004, 2004 12th European Signal Processing Conference.

[23]  LJubisa Stankovic,et al.  A measure of some time-frequency distributions concentration , 2001, Signal Process..

[24]  D. Konig,et al.  Application of cyclostationary and time-frequency signal analysis to car engine diagnosis , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[25]  MansinhaL..  Localization of the complex spectrum , 1996 .

[26]  Jin Jiang,et al.  Comparative study of three time-frequency representations with applications to a novel correlation method , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[28]  L. Stanković.  An analysis of some time-frequency and time-scale distributions , 1994 .