For spectral-temporal analysis of various non-stationary processes, it is proposed to use special tools - Weil-Heisenberg dual complex frames, which allow decomposing signals into fragments well-localized in time and frequency with the possibility of a more detailed spectral analysis of the signal in each selected time window. An algebraic method is being developed for the synthesis of such dual frames for discrete signals on a finite interval, allowing flexible tuning of the time-frequency resolution and fast computational implementation. The results of a computational experiment are presented, confirming the good properties of the obtained frames for detection-discrimination problems.
Weil-Heisenberg dual complex frame, optimal frame synthesis, good frequency-time localization, signal frame, efficient computational implementation, frequency-temporal resolution
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