Systems and methods for adaptive signal sampling and sample quantization for resource-constrained stream processing. Exemplary embodiments include a signal sampling and signal quantization method for a data stream from a ECG sensor into a pervasive device, the method including adaptively sampling the data stream, compressing data samples from the data stream, reducing the number of samples via quantization, defining a utility function for signal reconstruction, and formulating optimization on the reconstructed signal that is jointly sampled and quantized.

Systems and methods for adaptive signal sampling and sample quantization for resource-constrained stream processing

An animated display showing the Nativity scene. Human figures representing the Wise Men, shepherds, etc., move past the crib containing the infant Jesus. Each figure pauses, turns towards the crib, bows, turns back, and then moves away. The pausing action is created by a drive gear with some missing teeth. The turning action is created by two racks which mesh sequentially with a gear on which each figure is mounted. The bowing motion is created by a hinge mounting for each figure, and a push-rod actuation mechanism.

Adaptative signal sampling and sample quantization for resource-constrained stream processing

This paper presents novel results on the joint problem of sampling, reconstruction and quantization of analog signals Existing literature on this topic deals exclusively with band-limited signals in sampled form Our key departure from earlier results is that we deal with continuous time reconstruction of not necessarily band-limited signals Our approach utilizes concepts and tools from optimal sampled-data and receding horizon control theory The key conclusion from the work presented here is that, in the case under study, the optimal quantizer design problem can be partitioned into two sub-problems, namely (i) the design of an optimal analog pre-filter followed by sampling and (ii) an optimal quantizer, which works directly on the pre-sampled signals Simulation results are presented which illustrate the performance of the optimal A-D converter designed via these principles

Optimal AD-Conversion via Sampled-Data Receding Horizon Control Theory

In this thesis, the problem of analysis and design of Analog to Digital Converters (ADCs) is studied within an optimal feedback control framework. A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. The performance measure is defined as the worst-case average intensity of the filtered input-matching error, i.e., the frequency weighted difference between the input and output of the ADC. An exact analytic solution with conditions for optimality of a class of ADCs is presented in terms of the quantizer step size and range, resulting in a class of optimal ADCs that can be viewed as generalized Delta-Sigma Modulators (DSMs). An analytic expression for the performance of generalized DSMs is given. Furthermore, separation of quantization and control for this class of ADCs is proven under some technical conditions. When the technical conditions needed for establishing separation of quantization and control and subsequently optimality of the analytical solution to ADC design problem are not satisfied, suboptimal ADC designs are characterized in terms of solutions of a Bellman-type inequality. A computational framework is presented for designing suboptimal ADCs, providing certified upper and lower bounds on the performance. Thesis Supervisor: Alexandre Megretski Title: Professor of Electrical Engineering and Computer Science

Frequency selective analog to digital converter design : optimality, fundamental limitations, and performance bounds

In order that signals can be stored, transmitted or processed it is necessary that they first be converted into digital form. This, in turn, raises the problem of how to digitize data so as to achieve the best trade-off between data load and performance, i.e., "how to make the most out of a little". Two issues are involved in this problem, namely temporal quantization (i.e., sampling) and spatial quantization. These two problems have traditionally been addressed separately. Indeed, there exists substantial literature dealing with the temporal quantization problem, covering both band-limited and non-band-limited signals. The usual underlying paradigm is that of an analysis filter, followed by a sampler, followed by a reconstruction filter. Various parts of this architecture can be optimized once other parts have been specified. On the other hand, spatial quantization has been studied extensively for a given sampling strategy, particularly in the framework of sigma delta conversion. Finally, it is also possible to formulate the joint design problem for sampling and spatial quantization. This typically leads to enhanced performance compared to that achievable by considering the two aspects separately. This paper will survey the general area of sampling and quantization and analyze methods for achieving efficient data representations for signal processing and control applications. We will show how, on the one hand, contemporary control theory can contribute to the design of sampling and quantization systems and, on the other hand, how these systems impact on the performance of modern feedback control systems.

/pdf/efficient-data-representations-for-signal-processing-and-43tsngqquc.pdf

Efficient Data Representations for Signal Processing and Control: "Making Most of a Little"

This paper presents novel results on the joint problem of sampling and quantization of non bandlimited signals. Existing literature typically focuses either on sampling in the absence of quantization, or, conversely, studies quantization for already sampled signals. Our emphasis here is on the issues that arise at the intersection of these two design problems. We argue that the joint problem can be formulated and solved to any desired level of accuracy, using moving horizon optimization methods. We present several examples which show that consideration of the combined sampling and quantization problem gives important performance gains, relative to strategies which don't specifically address the interaction between these two problems.

Quantization and Sampling of Not Necessarily Band-Limited Signals

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Quantization and Sampling of Not Necessarily Band-Limited Signals