On Simple Oversampled A/D Conversion in L2(R)

TY - JOUR

T1 - On Simple Oversampled A/D Conversion in L2(R)

AU - Cvetkovic, Z

AU - Vetterli, M

PY - 2001/1

Y1 - 2001/1

N2 - The accuracy of oversampled analog-to-digital (A/D) conversion, the dependence of accuracy on the sampling interval τ and on the bit rate R are characteristics fundamental to A/D conversion but not completely understood. These characteristics are studied for oversampled A/D conversion of band-limited signals in L2 (R). We show that the digital sequence obtained in the process of oversampled A/D conversion describes the corresponding analog signal with an error which tends to zero as τ2 in energy, provided that the quantization threshold crossings of the signal constitute a sequence of stable sampling in the respective space of band-limited functions. Further, we show that the sequence of quantized samples can be represented in a manner which requires only a logarithmic increase in the bit rate with the sampling frequency, R=O(|logτ|), and hence that the error of oversampled A/D conversion actually exhibits an exponential decay in the bit rate as the sampling interval tends to zero

AB - The accuracy of oversampled analog-to-digital (A/D) conversion, the dependence of accuracy on the sampling interval τ and on the bit rate R are characteristics fundamental to A/D conversion but not completely understood. These characteristics are studied for oversampled A/D conversion of band-limited signals in L2 (R). We show that the digital sequence obtained in the process of oversampled A/D conversion describes the corresponding analog signal with an error which tends to zero as τ2 in energy, provided that the quantization threshold crossings of the signal constitute a sequence of stable sampling in the respective space of band-limited functions. Further, we show that the sequence of quantized samples can be represented in a manner which requires only a logarithmic increase in the bit rate with the sampling frequency, R=O(|logτ|), and hence that the error of oversampled A/D conversion actually exhibits an exponential decay in the bit rate as the sampling interval tends to zero

U2 - 10.1109/18.904518

DO - 10.1109/18.904518

M3 - Article

VL - 47

SP - 146

EP - 154

JO - IEEE TRANSACTIONS ON INFORMATION THEORY

JF - IEEE TRANSACTIONS ON INFORMATION THEORY

IS - 1

ER -