Analysis of errors in quantization of Weyl-Heisenberg frame expansions and oversampled A/D conversion

Manifestations of robustness of overcomplete expansions, acquired as a result of the redundancy, have been observed for two primary sources of degradation: white additive noise and quantization. These two cases require different treatments since quantization error has a certain structure which is obscured by statistical analysis. The central issue of this paper is a deterministic approach to quantization error analysis, with a focus on redundant Weyl-Heisenberg expansions in L²(R). This analysis demonstrates that overcomplete expansions exhibit a higher degree of robustness to quantization error than to a white additive noise, and indicates how this additional robustness can be exploited for improvement of representation accuracy. Further, it shows that under reasonable assumptions quantization error in Weyl-Heisenberg frame expansions can be reduced as ||e||² =O(1/r²), where r is the frame redundancy factor