Coarse quantization of highly redundant time–frequency representations of square-integrable functions

We introduce a family of coarse quantization algorithms for heavily oversampled Gabor expansions of certain classes of functions in L2(R). These algorithms, which we call the TF quantization algorithms, are inspired by sigma–delta modulation, a widely implemented coarse quantization scheme for oversampled bandlimited functions. We show that the TF algorithms produce weak type approximations where modulation spaces M m with suitable weight functions m are the appropriate test function spaces. We also show that the TF algorithms are translation invariant up to some uniform correction.  2003 Elsevier Science (USA). All rights reserved.