Celebratio Mathematica — Daubechies

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I. Daubechies, S. Güntürk, Y. Wang, and Ö. Yılmaz: “The Golden ratio encoder,” IEEE Trans. Inform. Theory 56 : 10 (2010), pp. 5097–5110. MR 2808667 Zbl 1366.94231 ArXiv 0809.1257 article

This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with \[ \beta = \phi = \frac{1 + \sqrt{5}}2 ,\] the golden ratio. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. Furthermore, a formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed.

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