Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept
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The continuous Gabor wavelet transform (GWT) has been utilized as an effective and powerful time-frequency analysis tool for identifying the rapidly-varying characteristics of some dispersive wave signals. The effectiveness of the GWT is strongly influenced by the wavelet shape that controls the time-frequency localization property. Therefore, it is very important to choose the right Gabor wavelet shape for given signals. Because the characteristics of signals are rarely known in advance, the determination of the optimal shape is usually difficult. Based on this observation, we aim at developing a systematic method to determine the signal-dependent shape of the Gabor wavelet for the best time-frequency localization. To find the optimal Gabor wavelet shape, we employ the notion of the Shannon entropy that measures the extent of signal energy concentration in the time-frequency plane. To verify the validity of the present approach, we analyze a set of elastic bending wave signals generated by an impact in a solid cylinder.
Key WordsContinuous Gabor wavelet transform optimal shaping factor time-frequency localization Shannon entropy function
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