Optimal Complex Morlet Wavelet Parameters for Quantitative Time-Frequency Analysis of Molecular Vibration

Abstract

When the complex Morlet function (CMOR) is used as a wavelet basis, it is necessary to select optimal bandwidth and center frequency. However, the method to select the optimal CMOR wavelet parameters for one specific frequency is still unclear. In this paper, we deeply investigate the essence of CMOR wavelet transform and clearly illustrate the time-frequency resolution and edge effect. Then, the selection method of the optimal bandwidth and center frequency is proposed. We further perform the quantitative time-frequency (QTF) analysis of water molecule vibration based on our method. We find that the CMOR wavelet parameters obtained by our method can not only meet the requirement of frequency resolution but also meet the limit of edge effect. Moreover, there is an uphill energy relaxation in the vibration of the water molecule, which agrees well with the experimental results. These results demonstrate that our method can accurately find the optimal CMOR wavelet parameters for the target frequency.