Celebratio Mathematica

R. Balan, I. Daubechies, and V. Vaishampayan: “The analysis and design of windowed Fourier frame based multiple description source coding schemes,” IEEE Trans. Inform. Theory 46 : 7 (2000), pp. 2491–2536. MR 1806816 Zbl 0998.94011 article

In this paper the windowed Fourier encoding-decoding scheme applied to the multiple description compression problem is analyzed. In the general case, four window functions are needed to define the encoder and decoder, although this number can be reduced to three or two by using time-shift or frequency-shift division schemes. The encoding coefficients are next divided into two groups according to the eveness of either the modulation or translation index. The distortion on each channel is analyzed using the Zak transform. For the optimal windows, explicit representation formulas are obtained and nonlocalization results are proved. Asymptotic formulas of the total distortion and transmission rate are established and the redundancy is shown to trade off between these two.

Radu Victor Balan	Related
Vinay A. Vaishampayan	Related

I. Daubechies, R. DeVore, C. S. Güntürk, and V. A. Vaishampayan: “Beta expansions: A new approach to digitally correct A/D conversion,” pp. 784–787 in 2002 IEEE international symposium on circuits and systems: Proceedings (Phoenix-Scottsdale, AZ, 26–29 May 2007), vol. 2. IEEE (Piscataway, NJ), 2002. incollection

We introduce a new architecture for pipelined (and also algorithmic) A/D converters that give exponentially accurate conversion using inaccurate comparators. An error analysis of a sigma-delta converter with an imperfect comparator and a constant input reveals a self-correction property that is not inherited by the successive refinement quantization algorithm that underlies both pipelined multistage A/D converters and algorithmic A/D converters. Motivated by this example, we introduce a new A/D converter, the beta converter, which has the same self-correction property as a sigma-delta converter but which exhibits higher order (exponential) accuracy with respect to the bit rate as compared to a sigma-delta converter, which exhibits only polynomial accuracy.

Ronald Alvin DeVore	Related
Cemalettin Sinan Güntürk	Related
Vinay A. Vaishampayan	Related

I. Daubechies, R. A. DeVore, C. S. Güntürk, and V. A. Vaishampayan: “A/D conversion with imperfect quantizers,” IEEE Trans. Inform. Theory 52 : 3 (2006), pp. 874–885. MR 2238058 Zbl 1231.94036 article

This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog-to-digital (A/D) converters such as pulse code modulation (PCM) and sigma–delta (\( \Sigma\Delta \)) modulation. \( \Sigma\Delta \) modulation, which is based on coarse quantization of oversampled (redundant) samples of a signal, enjoys a type of self-correction property for quantizer threshold errors (bias) that is not shared by PCM. Although “classical” \( \Sigma\Delta \) modulation is inferior to PCM in the rate-distortion sense, this robustness feature is believed to be one of the reasons why \( \Sigma\Delta \) 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 self-correction property, but that achieve higher order accuracy relative to bit rate compared to classical \( \Sigma\Delta \). More precisely, two different types of encoders are introduced that exhibit exponential accuracy in the bit rate (in contrast to the polynomial-type accuracy of classical \( \Sigma\Delta \)) while possessing the self-correction property.

Ronald Alvin DeVore	Related
Cemalettin Sinan Güntürk	Related
Vinay A. Vaishampayan	Related

year	title	people

			clear

Ingrid Daubechies

Complete Bibliography

Works connected to Vinay A. Vaishampayan

Filter the Bibliography List