WAVELET ANALYSIS - BASIC THEORY AND SOME APPLICATIONS

The basic theory of the wavelet transform, an effective investigation tool for inhomogeneous processes involving widely different scales of interacting perturbations, is presented. In contrast to the Fourier tr ansform, with the analysing function extending over the entire axis of time, the two-parametric analysing function of the one-dimensional wa velet transform is well localised in both time and frequency, The pote ntial of the method is illustrated by analysing familiar model series (such as harmonic, fractal, and those with various types of singularit ies) and the long-term variation of some meteorologic characteristics (Southern oscillation index and global and hemispheric temperatures). The analysis of a number of El-Nino events and of the temporal behavio ur of the Southern oscillation index reveals periodic components, loca l periodicity features, and time scales on which self-similarity struc tures are seen. On the whole, both stochastic and regular components s eem to be present. The global and hemispheric temperatures are qualita tively similar in structure, the main difference-presumably due to the greater amount of land and stronger anthropogenic factor-being that t he warming trend in the Northern hemisphere is slightly stronger and g oes first in time.