Abstract

Force variables and other signals are recorded as time series. These recorded data contain time and frequency information and most of the data also contain some disturbing noise. The purpose of this presentation is to show the decomposition of a time series into the wavelet-transformed signal and its high- and low-complement using only a single specified resolution wavelet. This is beneficial because two of the resulting components, both the high complement (representing vibrations of the skis) and the low complement (representing forces produced during skiing) are of value. The third component (the wavelet-transformed signal) is the noise which is extracted from the signal. Decomposition reflects that all three components, the wavelet-transformed signal and its high- and low-complement, are additive and reconstitute the original time series. The decomposition is achieved using a specified resolution wavelet: a wavelet with a predefined time and frequency resolution. A wavelet of the authors' choice will be used for this analysis without considering that other wavelet types could be as valuable. The time series of the three components will be compared with time series obtained by other filtering and smoothing techniques. How this decomposition differs from established filtering techniques and what advantages it has is of interest. The decomposition represents a first step of a full wavelet analysis. However instead of using additional wavelets to cover higher and lower frequency ranges, only high and low complements will be considered. A full comparison with multi resolution wavelet analysis would exceed the scope of this presentation, however, some features will be discussed. The aim is to use the specified wavelet analysis in a form as simple as sliding averages but with greater insight into the properties of the recorded time series. The decomposition of the signal by a specified resolulion wavelet is an application of known filtering procedures and the underlying features result from the properties of Fourier - transforms. However, one is often not aware of the filtering features in both the time- and frequency-domain. Therefore, extended examples will be used to increase this awareness. Einleitung (gekürzt und geändert)