Abstract
To build effective methods of approximation and spectral-temporal analysis of various processes, we propose special tools - complex Weyl-Heisenberg signal frames, which allow decomposing signals to components that are well localized simultaneously in time and frequency The chosen optimality criterion ensures the construction of a tight signal frame with the lowest standard deviation of frame functions from the desired standard. In addition, a special algebraic structure of the synthesis algorithm in the form of a product of sparse matrices allows for efficient computational implementation and flexible adjustment of the frequency-time resolution of the signal functions of the frame. The results of the experiment confirming the effective computational implementation of the algorithm and a good time-frequency localization of frame functions are presented.
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