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

摘要

We introduce a family of coarse quantization algorithms for heavily oversampled Gabor expansions of certain classes of functions in L~2(R). These algorithms, which we call the TFΣΔ quantization algorithms, are inspired by sigma―delta modulation, a widely implemented coarse quantization scheme for oversampled bandlimited functions. We show that the TFΣ Δ algorithms produce weak type approximations where modulation spaces M_,~(1,1) with suitable weight functions m are the appropriate test function spaces. We also show that the TFΣ Δ algorithms are translation invariant up to some uniform correction.