On simple oversampled A/D conversion in L/sup 2/(R)

The accuracy of oversampled analog-to-digital (A/D) conversion, the dependence of accuracy on the sampling interval /spl tau/ 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 L/sup 2/ (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 /spl tau//sup 2/ 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(|log/spl tau/|), 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.