On simple oversampled A/D conversion in L-2(IR)
Accuracy of oversampled analog-to-digital (AID) Conversion, the dependence of accuracy on the sampling interval tau and on the bit rate R are characteristics fundamental to AID conversion but not completely understood. These characteristics are studied in this paper for oversampled A/D conversion of band-limited signals in L-2(IR). 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 tau (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 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.
oversampling conversion accuracy analog-to-digital (aid)