Wavelets for the space-time structure analysis of physical fields

Abstract

Spectral analysis, based on the Fourier method, is a general tool in physics. Wavelets appeared as a natural generalization of classical spectral analysis to the case of complex nonstationary and spatially inhomogeneous systems, for which a comparison with an infinite sinusoid, which forms the basis of the Fourier method, has to be replaced by a comparison with a finite wave packet, which is known as a wavelet. In this review, the authors, based largely on their own experience of application wavelet analysis in astro- and geophysics, solar-terrestrial relations, as well as climatology, medical physics, and laboratory hydrodynamic experiments, demonstrate the possibilities and discuss the practical aspects of the application of the wavelet apparatus to the interpretation of signals and images of various physical natures.