Convergence of an iterative time-variant filtering based on discrete Gabor transform

An iterative time-variant filtering based on the discrete Gabor transform (DGT) has been recently proposed by the authors. In this correspondence, we present a proof of the convergence of the iterative algorithm under a sufficient condition on the analysis and synthesis window functions of the DGT. In the meantime, we show that the iterative algorithm refines the least squares solution.