The golden ratio encoder

Authors:
Ingrid Daubechies;C. Sinan Güntürk;Yang Wang;Özgür Yilmaz
Affiliations:
Department of Mathematics and the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ;Courant Institute of Mathematical Sciences, New York University, New York, NY;Department of Mathematics, Michigan State University, East Lansing, MI;Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 3
Cited 0

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A/D conversion with imperfect quantizers

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Robust and Practical Analog-to-Digital Conversion With Exponential Precision

IEEE Transactions on Information Theory

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Abstract

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 β = Φ = (1 + √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.