Time-Frequency Fading Algorithms Based on Gabor Multipliers

In this paper, we address a particular instance of time-frequency filter design, which call Time-Frequency Fading (TFF). TFF the only available information concerns localization component to be filtered out or attenuated: signal interest is supposed spread in plane, whereas perturbation concentrated within specified region Ω. The problem formulated as an optimization designed fade with accurate control on fading level. corresponding objective function involves data fidelity term that aims match TF coefficients estimated those observed outside support. It also penalty controls energy reconstructed signal, region. We obtain closed-form solution Gabor multipliers, i.e. linear operators pointwise product by transfer called mask. study properties dominant eigenvectors these attention case where Ω disjoint union several sub-regions. decay eigenvalues naturally lead reduced-rank approximations, and further approximations are obtained multiply connected case. Also, exploit random projection methods speed up eigenvalue decompositions rank reduction. This implemented two algorithms, cover cases single multiple regions. efficiency proposed approach demonstrated audio signals perturbations while leading good quality reconstruction.