Analog to digital conversion for finite frames

John J. Benedetto; Alexander M. Powell; Ozgur Yilmaz

doi:10.1117/12.612909

17 September 2005 Analog to digital conversion for finite frames

John J. Benedetto, Alexander M. Powell, Ozgur Yilmaz

Proceedings Volume 5914, Wavelets XI; 591416 (2005) https://doi.org/10.1117/12.612909
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

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)/N^1.25 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.

Citation Download Citation

John J. Benedetto, Alexander M. Powell, and Ozgur Yilmaz "Analog to digital conversion for finite frames", Proc. SPIE 5914, Wavelets XI, 591416 (17 September 2005); https://doi.org/10.1117/12.612909

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