Wavelet transform for analysis of molecular dynamics

The wavelet transform (WT) is suggested as an analysis tool in molecular dynamics by analogy with its use in signal and image processing. In particular, the WT excels in detecting rare events such as transitions that are localized in both time and frequency. Coupled with this property, the WT is also an efficient method for separating phenomena of different time scales. In this regard, the WT permits filtering out the high-frequency noise without completely omitting the high-frequency phenomena whose contribution is crucial in cases where the dynamics is localized in frequency and time. Two time series are studied, resulting respectively from the deterministic dynamics of a three-dimensional polymer chain and the stochastic dynamics of a one-dimensional polymer model subjected to random forces within the Langevin equation formalism. The WT is observed to excel in reconstructing the original signal by a subset of the basis used in the analysis and in identifying the occurrence of rare phenomena by examining the wavelet energies at high-resolution levels.