An adaptive Generalized S-transform for instantaneous frequency estimation

The Generalized S-transform (GST) applied in Instantaneous Frequency (IF) estimation is addressed in this paper. The analytical model for IF estimation error using the GST is established, which reveals that the estimation bias is determined directly by two variables: the standard deviation of the Gaussian window and the Instantaneous Frequency Rate (IFR) of the test signal. Based on the mathematical model, performance of the GST as an IF estimator is analyzed by three steps. Firstly, the time-varying expression for IF estimation Relative Error (RE) using the GST is derived. Secondly, the relationships between the RE and the signal's frequency characters are found. Thirdly, the effects of the window parameters on the RE are discussed. Consequently, a novel Adaptive Generalized S-transform (AGST) is developed, in which the window parameters are automatically adjusted in order to process signals with fast changing frequency characters. The proposed method is evaluated through several kinds of test signals to show its efficiency in IF estimation.

[1]  LJubisa Stankovic,et al.  Instantaneous frequency estimation by using the Wigner distribution and linear interpolation , 2003, Signal Process..

[2]  R. P. Lowe,et al.  Local S-spectrum analysis of 1-D and 2-D data , 1997 .

[3]  Robert Glenn Stockwell,et al.  A basis for efficient representation of the S-transform , 2007, Digit. Signal Process..

[4]  Juan José Dañobeitia,et al.  The $S$-Transform From a Wavelet Point of View , 2008, IEEE Transactions on Signal Processing.

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

[6]  Shubha Kadambe,et al.  A comparison of the existence of 'cross terms' in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform , 1992, IEEE Trans. Signal Process..

[7]  Jin Jiang,et al.  Time-frequency feature representation using energy concentration: An overview of recent advances , 2009, Digit. Signal Process..

[8]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[9]  Jin Jiang,et al.  A Window Width Optimized S-Transform , 2008, EURASIP J. Adv. Signal Process..

[10]  Jin Jiang,et al.  Instantaneous Frequency Estimation Using the ${\rm S}$ -Transform , 2008, IEEE Signal Processing Letters.

[11]  Jin Jiang,et al.  Frequency-based window width optimization for S-transform , 2008 .

[12]  Mostefa Mesbah,et al.  IF estimation for multicomponent signals using image processing techniques in the time-frequency domain , 2007, Signal Process..

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

[14]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[15]  LJubisa Stankovic,et al.  Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length , 1998, IEEE Trans. Signal Process..

[16]  Ljubisa Stankovic,et al.  Performance of quadratic time-frequency distributions as instantaneous frequency estimators , 2003, IEEE Trans. Signal Process..

[17]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[18]  LJubisa Stankovic,et al.  A measure of some time-frequency distributions concentration , 2001, 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]  P. McFadden,et al.  DECOMPOSITION OF GEAR VIBRATION SIGNALS BY THE GENERALISED S TRANSFORM , 1999 .

[21]  C. Robert Pinnegar.  A new subclass of complex-valued S-transform windows , 2006, Signal Process..