Wavelet filtering with high time-frequency resolution and effective numerical implementation applied on polar motion

摘要

Polar motion consists of two main signal components: the Chandler wobble and the annual oscillation. In particular the Chandler wobble is characterized by a time-varying energy behavior, i.e. the amplitude and the frequency are time-dependent functions. Since wavelet analysis is an appropriate tool for the detection of signal components with time-varying amplitudes and/or frequencies, wavelet transform tools may be used for the extraction or filtering of a desired signal component. Furthermore, due to the fact that the Chandler period is relatively close to one year, high resolution wavelet analysis with respect to the time-frequency domain is required. Thus, the complex valued Morlet wavelet function is qualified, since it is characterized by the smallest possible time-frequency window. Due to the fact that the Morlet wavelet is non-orthogonal, the filter bank techniques for orthogonal wavelets fail. This gave reason to create a filter bank based on the Morlet wavelet to provide both, high resolution and very effective numerical implementation. It is obvious that the wavelet transform of the filtered signal shall recover the manipulated wavelet coefficients as close as possible. Thus, the filtered signal may be determined by means of a least-squares adjustment. In this paper an effective algorithm is presented which makes use of the efficiency of the analysis filter bank. Using the described method, signal components can be extracted from a given data set with maximal achievable accuracy in short time. An example is presented, which enables a Morlet wavelet based representation of the Chandler wobble derived from the IERS polar motion time series.