Random Time-Varying Filtering

Tag / Zeit: 16.08.2021, 15:20-15:40
Typ: Regulärer Vortrag
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Zusammenfassung: Time-varying filtering is of crucial importance in many areas of signal processing and, in particular, in audio processing. From a mathematical point of view, time-varying filters correspond to so-called "frame multipliers". Here, the audio signal is first transformed into another signal domain, typically by means of a time-frequency transformation; then, the resulting transformed signal coefficients are multiplied with a "symbol"; and, finally, an audio signal is re-synthesized. Depending on the choice of the symbol, a frame multiplier allows to amplify certain audio components and/or to suppress others. In this contribution, we consider frame multipliers, whose symbols are chosen at random. We show that the corresponding random time-varying filters satisfy remarkable mathematical properties. Moreover, we demonstrate that they are highly efficient for signal compression. Our analysis is based on the recent mathematical methodology "compressive sensing".