The golden ratio encoder

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

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number5571869
Pages (from-to)5097-5110
Number of pages14
JournalIEEE Transactions on Information Theory
Volume56
Issue number10
DOIs
StatePublished - Oct 2010

Fingerprint

Analog to digital conversion
multiplier
Values

Keywords

  • 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

Cite this

Daubechies, I., Gunturk, C. S., Wang, Y., & Yilmaz, Ö. (2010). The golden ratio encoder. IEEE Transactions on Information Theory, 56(10), 5097-5110. [5571869]. https://doi.org/10.1109/TIT.2010.2059750

The golden ratio encoder. / Daubechies, Ingrid; Gunturk, C. Sinan; Wang, Yang; Yilmaz, Özgr.

In: IEEE Transactions on Information Theory, Vol. 56, No. 10, 5571869, 10.2010, p. 5097-5110.

Research output: Contribution to journalArticle

Daubechies, I, Gunturk, CS, Wang, Y & Yilmaz, Ö 2010, 'The golden ratio encoder', IEEE Transactions on Information Theory, vol. 56, no. 10, 5571869, pp. 5097-5110. https://doi.org/10.1109/TIT.2010.2059750
Daubechies, Ingrid ; Gunturk, C. Sinan ; Wang, Yang ; Yilmaz, Özgr. / The golden ratio encoder. In: IEEE Transactions on Information Theory. 2010 ; Vol. 56, No. 10. pp. 5097-5110.
@article{3e66eeaf1cd54c94b95ad916e1492954,
title = "The golden ratio encoder",
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.",
keywords = "Analog-to-digital conversion, beta encoders, beta expansions, golden ratio, quantization, robustness",
author = "Ingrid Daubechies and Gunturk, {C. Sinan} and Yang Wang and {\"O}zgr Yilmaz",
year = "2010",
month = "10",
doi = "10.1109/TIT.2010.2059750",
language = "English (US)",
volume = "56",
pages = "5097--5110",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "10",

}

TY - JOUR

T1 - The golden ratio encoder

AU - Daubechies, Ingrid

AU - Gunturk, C. Sinan

AU - Wang, Yang

AU - Yilmaz, Özgr

PY - 2010/10

Y1 - 2010/10

N2 - 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.

AB - 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.

KW - Analog-to-digital conversion

KW - beta encoders

KW - beta expansions

KW - golden ratio

KW - quantization

KW - robustness

UR - http://www.scopus.com/inward/record.url?scp=77956655082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956655082&partnerID=8YFLogxK

U2 - 10.1109/TIT.2010.2059750

DO - 10.1109/TIT.2010.2059750

M3 - Article

VL - 56

SP - 5097

EP - 5110

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 10

M1 - 5571869

ER -