Nakonechny A. Development of Theory and Practice of Mathematical Modelling of Signals in Time-frequency Domain.

The thesis is dedicated to the development of theoretical statements of signals representation in time-frequency domain. The new direction of wideband signals representation in wavelet domain, which provides a number of advantages over existent representations, is generalized and developed. There have been developed separate theses of theory of time-frequency representation of images signals and space-frequency quantization of wavelet coefficients that allowed to improve quality and compression ratio of such signals. The methods of embedding image watermarking into black-and-white and color images in wavelet domain are improved. The research results confirm high tolerance of watermarked signals of compression, filtering and geometric distortions. There have been elaborated the new methods and mathematical models of processes of signals power parameters measurement on the basis of their time-frequency transform, high accuracy and noise immunity of which are confirmed by research results. The results ofwork are used for construction of new firmware means of data acquisition and processing systems of digital information.