Novel Inverse S Transform in Time-Frequency Filtering with Energy Concentration Enhancement and Side Effects Elimination
Date Issued
2010
Date
2010
Author(s)
Wang, Pai-Wei
Abstract
The S transform is a powerful linear time-frequency distribution with a progressive resolution. It has been shown useful in various fields of applications. Since it is linear, it filters efficiently in a time-frequency domain by multiplying a mask function. There exist several different inverse algorithms, which result in different filtering effects. The conventional inverse S transform proposed by Stockwell et al. is efficient but suffers from time leakage during filtering. The recent algorithm proposed by Schimmel and Gallart has better time localization during filtering but suffers from a reconstruction error and the frequency leakage. In this dissertation, we propose two new inverse S transforms with equalization filters that compensate the distortion resulted from the previous two methods during filtering. Besides, we also derive the transformation matrices of the S transform and two novel least square inverse algorithms. The first one minimizes the global mean squared error of the entire time-frequency spectrum, and the second one considers only the specific interesting time-frequency regions and is more flexible. Experimental results show that the proposed inverse S transforms provide more stable and better performance in time-frequency filtering than the existing ones.
Recently researchers noticed that the conventional discrete S transforms are not equivalent in the time and the frequency domains, which may result in unreliable time-frequency information and confuse researchers. The solution thus far has some drawbacks and is unsatisfactory. In this dissertation, a new discrete S transform adopting the folded windows is proposed to eliminate the side effects of discretizing. This new discrete S transform has the theoretical importance that the time version and frequency version are equivalent and therefore provides more reliable information than previous solutions. Furthermore, it inherits the properties from the continuous S transform more completely.
Another important improvement we made to the S transform is to enhance the energy concentration. Based on the concentration measure, Djurović et al. proposed a method to optimize the window width in the S transform. However, it is found that although their method performs well for the high and middle frequency signals, it may fail for the low frequency ones. In this dissertation, a new method, which is more flexible than the previous one, is proposed to deal with this problem. Comparison of these two methods for energy concentration enhancement is also provided. Experimental result shows that the proposed method achieves higher energy concentration in comparison to the previous one and the original ST.
Subjects
S Transform
Time-Frequency Analysis
Type
thesis
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