access icon free Signal recognition and adapted filtering by non-commutative tomography

Tomogram, a generalisation of the Radon transform to arbitrary pairs of non-commuting operators, is a positive bilinear transforms with a rigorous probabilistic interpretation which provides a full characterisation of the signal and is robust in the presence of noise. Tomograms based on the time–frequency operator pair, were used in the past for component separation and denoising. Here the authors show that, even for noisy signals, meaningful time-resolved information may be obtained by the construction of an operator pair adapted to the signal.

Inspec keywords: probability; adaptive filters; signal processing

Other keywords: positive bilinear transforms; time-frequency operator pair; adapted filtering; rigorous probabilistic interpretation; time-resolved information; noncommuting operators; signal recognition; Radon transform; noncommutative tomography

Subjects: Filtering methods in signal processing; Signal processing theory; Other topics in statistics; Monte Carlo methods

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