Reduction of the MSE in R-times oversampled A/D conversion O(1/R) to O(1/R/sup 2/)

IEEE Trans. Inform. Theory

2001

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Abstract-Accuracy of oversampled analog-to-digital (A/D) conversion, the dependence of accuracy on the sampling interval and on the bit rate are characteristics fundamental to A/D conversion but not completely understood. These characteristics are studied in this paper for oversampled A/D conversion of band-limited signals in 2 ( ). 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 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, = ( log ), 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.

Section: Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Cvetković

IEEE Trans. Inform. Theory

2001

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“…However, it has been recently proved that the error-rate characteristics of oversampled A/D conversion can be drastically improved using non-linear reconstruction algorithms, referred to as consistent. More precisely, it can be shown [7] that for real periodic bandlimited signals of period T and having W = 2M + 1 non-zero Fourier coefficients, the reconstruction mean-squared error (MSE) behaves as O(1/r 2 ) as opposed to the O(1/r) given by Equation (12). This is provided that the number Q of quantization threshold crossings (QTC) in the interval [0, T ) is greater than W .…”

Section: Periodic Bandlimited Signalsmentioning

confidence: 99%

Distributed Compression in Acoustic Sensor Networks using Oversampled A/D Conversion

Roy

2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings

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We address the problem of distributed compression in acoustic sensor networks. A typical scenario consists of a set of microphones that record a sound source located at some unknown position. The goal then is to convey the corresponding audio signals to a central base station for processing. We thus aim at designing efficient distributed communication schemes that minimize the overall bit-rate needed in order to achieve a given reconstruction accuracy. In this paper, we show how the a priori knowledge of the system's geometry can be beneficially used in order to lower the transmission rates. We propose a distributed coding scheme for simple synthetic sources. These results are then applied to more general signals by means of oversampled analog-to-digital conversion. Simulation results confirm the effectiveness of our approach.

“…If a space of periodic bandlimited signals is considered, this condition is satisfied by any set of points as long as its cardinality is greater than or equal to the dimension of the space. The constant of proportionality K in (5) depends on the norm of f ( t ) in the respective space, and also on the distribution of its quantization threshold crossings [2], [3]. It is important to note that if f ( t ) is a periodic bandlimited signal, its digital representation allows for reconstruction with an error which either tends to zero with increased oversampling as lle(t)112 = O ( r 2 ) , or does not approach zero at all.…”

Section: IImentioning

confidence: 99%

“…In order to achieve reconstruction of a bandlimited signal f ( t ) with an error e ( t ) bounded as it is essential that samples taken at points of quantization threshold crossings of f ( t ) provide complete and stable description of the corresponding class of bandlimited signals [2], [3], [4]. If a space of periodic bandlimited signals is considered, this condition is satisfied by any set of points as long as its cardinality is greater than or equal to the dimension of the space.…”

Section: IImentioning

confidence: 99%

On error-rate characteristics of oversampled A/D conversion

Cvetković

Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97

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Abstract-Accuracy of simple A/D conversion1 can b e improved by refining either sampling interval or quantization step. Although t h e former is more convenient for implementation reasons, t h e l a t t e r seems t o b e more efficient. When t h e quantization s t e p tends t o zero for a fixed sampling interval, t h e expected value of t h e quantization error decays exponentially as a function of t h e bit-rate B, E(e(t)') = O(exp(-2aB)). On t h e other hand, if t h e oversampling ratio is increased for a fixed quantization s t e p t h e error behaves as E(e(t)') = O(l/B). We show t h a t this inferior error-rate performance of oversampled A/D conversion is a consequence of inadequate reconstruction a n d encoding, a n d propose a n efficient scheme for lossless encoding of quantized samples. W i t h this encoding scheme t h e error of oversampled A/D conversion decays exponentially with t h e bit-rate.