Lazorenko O. Modern analysis and processing of the ultra wideband processes.

The object is ultra wideband (UWB) processes in physics, radio physics, electronics and technologies. Тhe purpose is creation of new UWB signal classes, their mathematic modelling, application of new methods of analysis and processing of UWB signals and processes, real UWB process analysis in problems of physics (radio physics) of atmosphere and geospace. Тhe wavelet, wigner and choi-williams analysis, the atomic function theory, the system spectral analysis, the spectral analysis based on application of traditional one-dimensional and short-time Fourier transforms and of adaptive Fourier transform, the digital simulation method, the theoretical (analytical) method were applied. The new results are following. The wavelet analysis, the Wigner and Choi-Williams transforms were first proposed to processing of UWB signals and radio physic processes. New integral transform called as adaptive Fourier transform was created. Using wavelet analysis and Wigner transform, the problems of de-tection and reconstruction of ultra-short UWB process (signal) with additive weakly correlated noise presents were first solved. New UWB signal classes (fractal and non-linear UWB signals), which in a number of cases excel the ultra-short UWB signals on the possibilities, were developed. New analytical wavelets on the basis of Kravchenko-Rvachov mathematical models and new classes of Kravchenko-Wigner and Choi-Williams nonlinear transforms, which unite advan-tages of atomic functions with possibilities of wavetet , wigner and choi-williams analysis accordingly, were created. New synthetic method of analysis of signals and radio physic prosesses called as the system spectral analysis and based on joint application of row of linear and non-linear integral transforms was developed. The extent of application: the results are applied. The field of application: physics and radio physics of atmosphere and geospace.