Compensating for window effects in the calculation of spectrographic instantaneous bandwidth

Exact results derived by Cohen and Lee (1988-1990) are used to study the distortion induced by the window in the computation of instantaneous bandwidth via the spectrogram. These concepts have been recently used in an interesting study regarding lesion-induced blood flow disturbances, where an approximation was made to compensate for the window effects. We show that this compensation is accurate for stationary signals, but becomes increasingly poorer as the signal becomes less stationary (e.g., large frequency modulations). We propose an alternative technique to reduce the window distortions, and point out the use of other time-frequency distributions that do not suffer such distortions.

[1]  Zhi-Yue Lin,et al.  Time-frequency representation of the electrogastrogram-application of the exponential distribution , 1994, IEEE Transactions on Biomedical Engineering.

[2]  William J. Williams,et al.  Time-frequency analysis of electrophysiology signals in epilepsy , 1995 .

[3]  D. T. Barry,et al.  Time-frequency analysis of skeletal muscle and cardiac vibrations , 1996, Proc. IEEE.

[4]  M. Ruano,et al.  Nonstationarity broadening reduction in pulsed Doppler spectrum measurements using time-frequency estimators , 1996, IEEE Transactions on Biomedical Engineering.

[5]  Patrick J. Loughlin.  Moments and maximum entropy densities in time frequency , 1998, Optics & Photonics.

[6]  Leon Cohen,et al.  Instantaneous bandwidth for signals and spectrogram , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[7]  W. J. Williams,et al.  Cross Time-frequency Representation Of Electrocorticograms In Temporal Lobe Epilepsy , 1991 .

[8]  Patrick J. Loughlin,et al.  Instantaneous bandwidth of multicomponent signals , 1999, Optics & Photonics.

[9]  A. Barnes.  Instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data , 1993 .

[10]  Leon Cohen,et al.  Local Bandwidth And Optimal Windows For The Short Time Fourier Transform , 1989, Optics & Photonics.

[11]  Peter J. Fish,et al.  Correction for nonstationarity and window broadening in Doppler spectrum estimation , 1997, IEEE Signal Processing Letters.

[12]  M S Redfern,et al.  Time-varying characteristics of visually induced postural sway. , 1996, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[13]  Tzu-Hsien Sang,et al.  Adaptive RID kernels which minimize time-frequency uncertainty , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[14]  P. Loughlin,et al.  Positive local variances of time-frequency distributions and local uncertainty , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[15]  D. Barry,et al.  Muscle sounds are emitted at the resonant frequencies of skeletal muscle , 1990, IEEE Transactions on Biomedical Engineering.

[16]  L.-G. Durand,et al.  Comparison of time-frequency distribution techniques for analysis of simulated Doppler ultrasound signals of the femoral artery , 1994, IEEE Transactions on Biomedical Engineering.

[17]  D. T. Barry,et al.  Time-frequency transforms: a new approach to first heart sound frequency dynamics , 1992, IEEE Transactions on Biomedical Engineering.

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

[19]  Patrick J. Loughlin,et al.  Instantaneous frequency and time-frequency distributions , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[20]  W. J. Williams,et al.  Reduced interference distributions: biological applications and interpretations , 1996, Proc. IEEE.

[21]  Leon Cohen,et al.  Standard deviation of instantaneous frequency , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[22]  Leon Cohen,et al.  Instantaneous Frequency, Its Standard Deviation And Multicomponent Signals , 1988, Optics & Photonics.

[23]  S. Widmalm,et al.  Time frequency distributions of TMJ sounds. , 2008, Journal of oral rehabilitation.