Random Time-varying Filtering with Subsampling

Abstract

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 with an additional subsampling step of the output signal. We show that the corresponding subsampled 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”.