Math @ Duke

Publications [#287174] of Ingrid Daubechies
Papers Published
 Daubechies, I; DeVore, RA; Güntürk, CS; Vaishampayan, VA, A/D conversion with imperfect quantizers,
IEEE Transactions on Information Theory, vol. 52 no. 3
(2006),
pp. 874885, ISSN 00189448 [doi]
(last updated on 2018/05/20)
Abstract: This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analogtodigltal (A/D) converters such as pulse code modulation (PCM) and sigmadelta (∑Δ) modulation. ∑Δ modulation, which is based on coarse quantization of oversampled (redundant) samples of a signal, enjoys a type of selfcorrection property for quantizer threshold errors (bias) that is not shared by PCM. Although "classical" ∑Δ modulation is inferior to PCM in the ratedistortion sense, this robustness feature is believed to be one of the reasons why ∑Δ modulation is preferred over PCM in A/D converters with imperfect quantizers. Motivated by these facts, other encoders are constructed in this paper that use redundancy to obtain a similar selfcorrection property, but that achieve higher order accuracy relative to bit rate compared to classical ∑Δ. More precisely, two different types of encoders are introduced that exhibit exponential accuracy in the bit rate (in contrast to the polynomialtype accuracy of classical ∑Δ) while possessing the selfcorrection property. © 2006 IEEE.


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