On quantization of finite frame expansions: sigma-delta schemes of arbitrary order
Mark Lammers, Alexander M. Powell, Özgür Yılmaz · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
In this note we will show that the so called Sobolev dual is the minimizer over all linear reconstructions using dual frames for stable rth order ΣΔ quantization schemes under the so called White Noise Hypothesis (WNH) design criteria. We compute some Sobolev duals for common frames and apply them to audio clips to test their performance against canonical duals and another alternate dual corresponding to the well known Blackman filter.