The golden ratio encoder

Ingrid Daubechies, C. Sinan Güntürk, Yang Wang, Özgr Yilmaz

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number5571869
Pages (from-to)5097-5110
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2010


  • Analog-to-digital conversion
  • beta encoders
  • beta expansions
  • golden ratio
  • quantization
  • robustness

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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