Choi–Williams distribution function

Choi–Williams distribution function is one of the members of Cohen's class distribution function.[1] It was first proposed by Hyung-Ill Choi and William J. Williams in 1989. This distribution function adopts exponential kernel to suppress the cross-term. However, the kernel gain does not decrease along the axes in the ambiguity domain. Consequently, the kernel function of Choi–Williams distribution function can only filter out the cross-terms that result from the components that differ in both time and frequency center.

Mathematical definition

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The definition of the cone-shape distribution function is shown as follows:

 

where

 

and the kernel function is:

 


See also

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References

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  1. ^ E. Sejdić, I. Djurović, J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” Digital Signal Processing, vol. 19, no. 1, pp. 153-183, January 2009.
  • Time frequency analysis and wavelet transform class notes, Jian-Jiun Ding, the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, 2007.
  • S. Qian and D. Chen, Joint Time-Frequency Analysis: Methods and Applications, Chap. 5, Prentice Hall, N.J., 1996.
  • H. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE. Trans. Acoustics, Speech, Signal Processing, vol. 37, no. 6, pp. 862–871, June 1989.
  • Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shape kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. 38, no. 7, pp. 1084–1091, July 1990.