Asymptotically Exact Localized Expansions for Signals in Time-Frequency Domain
Aramazd H. Muzhikyan, Gagik T. Avanesyan
TL;DR
This paper introduces an exact mathematical method for analyzing signals in the time-frequency domain using a uniquely localized waveform, revealing the non-commutative geometry of the time-frequency plane.
Contribution
It presents a novel approach leveraging a strongly localized waveform to achieve asymptotically exact expansions in time-frequency analysis.
Findings
Provides a new waveform with strong exponential localization
Develops an exact method for time-frequency signal analysis
Visualizes signals using a novel graphical representation
Abstract
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in time-frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative geometry of the time-frequency plane. Signals are visualized using graphical representation constructed.
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