Analog to digital conversion for finite frames
John J. Benedetto, Alexander M. Powell, Özgür Yılmaz · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
Sigma-Delta (ΣΔ) schemes are shown to be an effective approach for quantizing finite frame expansions. Basic error estimates show that first order ΣΔ schemes can achieve quantization error of order 1/N, where N is the frame size. Under certain technical assumptions, improved quantization error estimates of order (logN)/N1.25 are obtained. For the second order ΣΔ scheme with linear quantization rule, error estimates of order 1/N2 can be achieved in certain circumstances. Such estimates rely critically on being able to construct sufficiently small invariant sets for the scheme. New experimental results indicate a connection between the orbits of state variables in ΣΔ schemes and the structure of constant input invariant sets.