Experimental analysis of pattern similarity between Bessel kernel and born-Jordan kernel

• Authors: Ming Li;Xue-Kang Gu;Wei Zhao
• Venue: ACACOS'08 Proceedings of the 7th WSEAS International Conference on Applied Computer and Applied Computational Science
• Year: 2008

Kernels play a role in time-frequency (TF) analysis of signals. Various types of kernels have been introduced in TF analysis. Usually, different types of kernels (i.e., kernels in different function form) correspond different types of TF distributions (TFDs). From a view of pattern matching, however, different TFDs may achieve the similar TFD result for a same signal if the used kernels are arranged such that they are similar in pattern under a certain condition. Essential issues in this regard are 1) which kernels may be similar in pattern and 2) under what conditions their patterns are similar. The answers to those issues are meaningful in TF analysis. As a stage work, this paper gives an experimental analysis of the pattern similarity between two types of kernels, the typical Born-Jordan kernel (i.e., Sinc kernel) and the Bessel one. Correlation coefficient is used to measure the pattern similarity. We present the correlation curve between them and propose the quantitative conditions that both kernels are similar and dissimilar. The analysis shows that the maximum similarity between them may reach 0.987 when the value of a scaling factor of Bessel kernel equals to 0.18. On the other hand, the minimum of the correlation between them is less than or equal to 0.55 when the scaling factor is less than or equal to 0.01. Hence, this paper suggests that Bessel kernel is more flexible than the typical Born-Jordan's in TF analysis. A case study is demonstrated.