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32
Statistical Theory of Quantization
 IEEE Trans. on Instrumentation and Measurement
, 1995
"... The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to flo ..."
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Cited by 38 (3 self)
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The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to floatingpoint quantization is demonstrated. Keywords  Quantization, noise model, quantization noise, noise spectrum, statistical theory, finite bit number, roundoff error, arithmetic rounding, floatingpoint quantization.
A CMOS Area Image Sensor With Pixel Level A/D Conversion
 IN ISSCC DIGEST OF TECHNICAL PAPERS
, 1995
"... A CMOS 64 x 64 pixel area image sensor chip using SigmaDelta modulation at each pixel for A/D conversion is described. The image data output is digital. The chip was fabricated using a 1.2µm two layer metal single layer poly nwell CMOS process. Each pixel block consists of a phototransistor and ..."
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Cited by 26 (7 self)
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A CMOS 64 x 64 pixel area image sensor chip using SigmaDelta modulation at each pixel for A/D conversion is described. The image data output is digital. The chip was fabricated using a 1.2µm two layer metal single layer poly nwell CMOS process. Each pixel block consists of a phototransistor and 22 MOS transistors. Test results demonstrate a dynamic range potentially greater than 93dB, a signal to noise ratio (SNR) of up to 61dB, and dissipation of less than 1mW with a 5V power supply.
Information Rates of Pre/Post Filtered Dithered Quantizers
 IEEE Trans. Information Theory
, 1997
"... We consider encoding of a source with a prespecified second order statistics, but otherwise arbitrary, by Entropy Coded Dithered (lattice) Quantization (ECDQ) incorporating linear preand postfilters. In the design and analysis of this scheme we utilize the equivalent additive noise channel model o ..."
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Cited by 19 (11 self)
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We consider encoding of a source with a prespecified second order statistics, but otherwise arbitrary, by Entropy Coded Dithered (lattice) Quantization (ECDQ) incorporating linear preand postfilters. In the design and analysis of this scheme we utilize the equivalent additive noise channel model of the ECDQ. For Gaussian sources and square error distortion measure, the coding performance of the pre/post filtered ECDQ approaches the ratedistortion function, as the dimension of the (optimal) lattice quantizer becomes large; actually, in this case the proposed coding scheme simulates the optimal forward channel realization of the ratedistortion function. For nonGaussian sources and finite dimensional lattice quantizers, the coding rate exceeds the ratedistortion function by at most the sum of two terms: the "information divergence of the source from Gaussianity" and the "information divergence of the quantization noise from Gaussianity". Additional bounds on the excess rate of the s...
Recursive Consistent Estimation with Bounded Noise
 IEEE TRANS. INFORM. TH
, 2001
"... Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such boundednoise estimation problems. The meansquare error (MSE) of the ..."
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Cited by 16 (11 self)
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Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such boundednoise estimation problems. The meansquare error (MSE) of the algorithm is "almost" (1/n²), where is the number of samples. This rate is faster than the (1/n) MSE obtained by standard recursive least squares estimation and is optimal to within a constant factor.
Deterministic Analysis of Oversampled A/D Conversion and Sigma/Delta Modulation, and Decoding Improvements using Consistent Estimates
, 1993
"... Analogtodigital conversion (ADC) which consists in a double discretization of an analog signal in time and in amplitude is increasingly used in modern data acquisition. However, the conversion process always implies some loss of information due to amplitude quantization. Oversampling is the techni ..."
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Cited by 6 (0 self)
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Analogtodigital conversion (ADC) which consists in a double discretization of an analog signal in time and in amplitude is increasingly used in modern data acquisition. However, the conversion process always implies some loss of information due to amplitude quantization. Oversampling is the technique currently used to reduce this loss of accuracy. The error reduction can be performed by lowpass filtering the quantized signal, thus eliminating the high frequency components of the quantization error signal. This is the classical method used to reconstruct the analog signal from its oversampled and quantized version. This reconstruction scheme yields a mean squared error (MSE) inversely proportional to the oversampling ratio R. The fundamental question pursued in this thesis is the following: how much information is available in the oversampled and quantized version of a bandlimited signal for its reconstruction? In order to identify this information, it is essential to go back to the original description of quantization which is typically deterministic. We show that a reconstruction scheme fully takes this information into account
Eldar, “Nonuniform sampling of periodic bandlimited signals: Part I–Reconstruction theorems,” submitted to
 IEEE Trans. Signal Processing
, 2004
"... Abstract—Digital processing techniques are based on representing a continuoustime signal by a discrete set of samples. This paper treats the problem of reconstructing a periodic bandlimited signal from a finite number of its nonuniform samples. In practical applications, only a finite number of val ..."
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Cited by 4 (0 self)
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Abstract—Digital processing techniques are based on representing a continuoustime signal by a discrete set of samples. This paper treats the problem of reconstructing a periodic bandlimited signal from a finite number of its nonuniform samples. In practical applications, only a finite number of values are given. Extending the samples periodically across the boundaries, and assuming that the underlying continuous time signal is bandlimited, provides a simple way to deal with reconstruction from finitely many samples. Two algorithms for reconstructing a periodic bandlimited signal from an even and an odd number of nonuniform samples are developed. In the first, the reconstruction functions constitute a basis while in the second, they form a frame so that there are more samples than needed for perfect reconstruction. The advantages and disadvantages of each method are analyzed. Specifically, it is shown that the first algorithm provides consistent reconstruction of the signal while the second is shown to be more stable in noisy environments. Next, we use the theory of finite dimensional frames to characterize the stability of our algorithms. We then consider two special distributions of sampling points: uniform and recurrent nonuniform, and show that for these cases, the reconstruction formulas as well as the stability analysis are simplified significantly. The advantage of our methods over conventional approaches is demonstrated by numerical experiments. Index Terms—Interpolation, nonuniform sampling, periodic signals, reconstruction, recurrent nonuniform sampling, stability, uniform sampling. I.
Analysis and Dynamic Range Enhancement of the AnalogtoDigital Interface in Multimode Radio Receivers
, 1997
"... The rapidly developing wireless market has spawned a multitude of different standards for cellular, PCS, and wireless data. To allow users the ability to access services conforming to disparate standards, multimode handsets capable of software reconfiguration are needed. These "software radios" are ..."
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Cited by 3 (0 self)
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The rapidly developing wireless market has spawned a multitude of different standards for cellular, PCS, and wireless data. To allow users the ability to access services conforming to disparate standards, multimode handsets capable of software reconfiguration are needed. These "software radios" are distinguished from their traditional counterparts by their strong reliance on digital channel filtering and demodulation which may be reprogrammed to receive different standards. In these radios, higher dynamic range is required from the analog portion, most notably, the analogtodigital converter (ADC). This
Reconstruction of periodic bandlimited signals from nonuniform samples
, 2004
"... I would first like to thank my advisor, Dr. Yonina Eldar, for her support, patience, and shoving me in the right direction in critical moments. Thank you for the knowledge I acquired from you. I feel extremely fortunate to have an advisor like you. Thanks to Prof. Arie Feuer of the Technion–Israel I ..."
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Cited by 3 (2 self)
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I would first like to thank my advisor, Dr. Yonina Eldar, for her support, patience, and shoving me in the right direction in critical moments. Thank you for the knowledge I acquired from you. I feel extremely fortunate to have an advisor like you. Thanks to Prof. Arie Feuer of the Technion–Israel Institute of Technology for first introducing me the field of nonuniform sampling. The initial step for this research was carried out from these fruitful discussions. Thanks to Prof. Amir Averbuch of the Tel Aviv University for raising the issue of stability of the algorithms proposed in this work. This topic stimulated the significant phase of my research. I want to also thank Prof. Michael Unser and Dr. Thierry Blu from EPFL, Swiss, and Dr. Thomas Strohmer from University of California, Davis for valuable suggestions related to this work. Thanks to every member of the research group under the supervision of Dr. Yonina Eldar. Ami, Liron, Zvika, Tsvika, Nagesh, Moshe, and Noam, I thank you all for your friendship, and for all the help through the endless discussions we had.
A 14bit 10MSamples/s D/A Converter Using Multibit  Modulation
 IEEE Journal of SolidState Circuits
, 1999
"... Abstract — A 14bit digitaltoanalog converter based on a fourthorder multibit sigma–delta modulator is described. The digital modulator is pipelined to minimize both its power dissipation and design complexity. The 6bit output of this modulator is converted to analog using 64 currentsteering ce ..."
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Cited by 2 (0 self)
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Abstract — A 14bit digitaltoanalog converter based on a fourthorder multibit sigma–delta modulator is described. The digital modulator is pipelined to minimize both its power dissipation and design complexity. The 6bit output of this modulator is converted to analog using 64 currentsteering cells that are continuously calibrated to a reference current. This converter achieves 85dB dynamic range at 5MHz signal bandwidth, with an oversampling ratio of 12. The chip was fabricated in a 0.5"m CMOS technology and operates from a single 2.5V supply. Index Terms — Current calibration, digitaltoanalog conversion, mixed analog–digital integrated circuits, multibit modulators, pipelined adders, sigma–delta modulation. I.