Celebratio Mathematica — Daubechies

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Z. Cvetkovic and I. Daubechies: “Single-bit oversampled A/D conversion with exponential accuracy in the bit-rate,” pp. 343–352 in Proceedings: Data compression conference 2000 (Snowbird, UT, 28–30 March 2000). Edited by J. A. Storer and M. Cohn. IEEE Computer Society Press (Los Alamitos, CA), 2000. Also published in IEEE Trans. Inform. Theory 53:11 (2007). incollection

James A. Storer	Related
Martin Cohn	Related
Zoran Dusan Cvetković	Related

Z. Cvetkovic, I. Daubechies, and B. F. Logan: “Interpolation of bandlimited functions from quantized irregular samples,” pp. 412–421 in Proceedings: Data compression conference (Snowbird, UT, 2–4 April 2002). Edited by J. A. Storer and M. Cohn. IEEE (Piscataway, NJ), 2002. incollection

The problem of reconstructing a \( \pi \)-bandlimited signal \( f \) from its quantized samples taken at an irregular sequence of points \( t_k \), \( k = \dots, -2 \), \( -1,0 \), \( 1,\dots \) arises in oversampled analog-to-digital conversion. The input signal can be reconstructed from the quantized samples \( f(t_k) \) by estimating samples \( f(n/\lambda) \), \( n = \dots,-2 \), \( -1,0 \), \( 1,\dots \), where \( \lambda \) is the average uniform density of the sequence \( (t_k) \), assumed here to be greater than one, followed by linear low-pass filtering. We study three techniques for estimating samples \( f(n/\lambda) \) from quantized irregular samples \( f(t_k) \), including Lagrangian interpolation, and two other techniques which result in a better overall accuracy of oversampled A/D conversion.

Benjamin F. Logan, Jr.	Related
Martin Cohn	Related
Zoran Dusan Cvetković	Related
James A. Storer	Related