Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates

Thao, Nguyen T.; Vetterli, Martin

doi:10.1109/78.277844

Cited by 105 publications

(72 citation statements)

References 12 publications

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“…It is known [21, p. 136] that, in the presence of additive zero-mean white measurement noise, oversampling by a factor of relative to the Nyquist rate leads to a reduction of noise variance in the reconstruction by a factor of . Similarly, with non-linear processing quantization noise can be reduced by a factor of (see, e.g., [22], [23], and references therein).…”

Section: E Noise Suppression Via Oversampling On Sensor Pathsmentioning

confidence: 99%

“…The spatial separation between two successive samples is approximately, which means that samples are taken farther apart in space when the sensor is moving fast. We also note from (22) that the effective spatial spread of the sampling kernel while obtaining sample is given by which means that samples obtained while the sensor is moving fast are obtained via a broader effective sampling kernel in space. It is also clear from (22) that the sampling kernel is also scaled down by a factor proportional to the velocity.…”

Section: F Non-uniform Sensor Speedsmentioning

confidence: 99%

“…We also note from (22) that the effective spatial spread of the sampling kernel while obtaining sample is given by which means that samples obtained while the sensor is moving fast are obtained via a broader effective sampling kernel in space. It is also clear from (22) that the sampling kernel is also scaled down by a factor proportional to the velocity. Now, since is bandlimited, it can be reconstructed exactly from its uniformly spaced samples by sinc interpolation.…”

Section: F Non-uniform Sensor Speedsmentioning

confidence: 99%

“…Denote by the output of the low-pass filter. We have where (22) Here is the velocity function, is the inverse function of , and . Thus at the output of the sampler, we get uniform samples at times .…”

Section: F Non-uniform Sensor Speedsmentioning

confidence: 99%

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Sampling and Reconstruction of Spatial Fields Using Mobile Sensors

Unnikrishnan

Vetterli

2013

IEEE Trans. Signal Process.

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Abstract-Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper, we study the emerging paradigm of sampling and reconstructing spatial fields using sensors that move through space. We show that mobile sensing offers some unique advantages over static sensing in sensing bandlimited spatial fields. Since a moving sensor encounters such a spatial field along its path as a time-domain signal, a time-domain anti-aliasing filter can be employed prior to sampling the signal received at the sensor. Such a filtering procedure, when used by a configuration of sensors moving at constant speeds along equispaced parallel lines, leads to a complete suppression of spatial aliasing in the direction of motion of the sensors. We analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter. We also analyze the effects of nonuniform sensor speeds on the reconstruction accuracy. Using simulation examples, we demonstrate the advantages of mobile sampling over static sampling in practical problems. We extend our analysis to sampling and reconstruction schemes for monitoring time-varying bandlimited fields using mobile sensors. We demonstrate that in some situations we require a lower density of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme. The exact advantage is quantified for a problem of sampling and reconstructing an audio field.Index Terms-Mobile sensors, spatial anti-aliasing, spatial field sampling and reconstruction.

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Section: E Noise Suppression Via Oversampling On Sensor Pathsmentioning

confidence: 99%

Section: F Non-uniform Sensor Speedsmentioning

confidence: 99%

Section: F Non-uniform Sensor Speedsmentioning

confidence: 99%

Section: F Non-uniform Sensor Speedsmentioning

confidence: 99%

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Sampling and Reconstruction of Spatial Fields Using Mobile Sensors

Unnikrishnan

Vetterli

2013

IEEE Trans. Signal Process.

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“…It is important to note that linear reconstruction does not provide the most accurate estimate x that can be obtained from the quantized coefficients. There are alternative methods to linear reconstruction, e.g., consistent reconstruction [16,29,13], which give smaller reconstruction error at the cost of greater complexity.…”

Section: Introductionmentioning

confidence: 99%

Alternative dual frames for digital-to-analog conversion in sigma–delta quantization

2008

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Abstract. We design alternative dual frames for linearly reconstructing signals from Sigma-Delta (Σ∆) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order Sigma-Delta quantizer produces approximations where the approximation error is at most of order 1/λ r , and λ > 1 is the oversampling ratio. We show that the counterpart of this result is not true for several families of redundant finite frames for R d when the canonical dual frame is used in linear reconstruction. As a remedy, we construct alternative dual frame sequences which enable an rth order Sigma-Delta quantizer to achieve approximation error of order 1/N r for certain sequences of frames where N is the frame size. We also present several numerical examples regarding the constructions.

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Deterministic analysis of sigma–delta modulation for linear and non-linear signal reconstruction

Thao

1997

Int. J. Circ. Theor. Appl.

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Deterministic analysis is becoming increasingly popular to study the theoretical mechanisms of ΣΔ modulation, as opposed to the classical noise‐shaping approach. This paper gives an overview of its application to the specific problem of signal reconstruction. Once an input signal has been processed through a ΣΔ modulator of given specifications, the fundamental question is to know what deterministic information can be retrieved about this signal from the ΣΔ output. The paper summarizes all results obtained in this research under a unified presentation framework. © 1997 by John Wiley & Sons, Ltd.

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Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates

Cited by 105 publications

References 12 publications

Sampling and Reconstruction of Spatial Fields Using Mobile Sensors

Sampling and Reconstruction of Spatial Fields Using Mobile Sensors

Alternative dual frames for digital-to-analog conversion in sigma–delta quantization

Deterministic analysis of sigma–delta modulation for linear and non-linear signal reconstruction

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