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Given an mtimesN matrix Phi, with m&lt;N, the system of equations Phix=y is typically underdetermined and has infinitely many solutions. Various forms of optimization can extract a "best" solution. One of the oldest is to select the one with minimal lscr<sub>2</sub> norm. It has been shown that in many applications a better choice is the minimal(More)
This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog-to-digital (A/D) converters such as pulse code modulation (PCM) and sigma-delta (SigmaDelta) modulation. SigmaDelta modulation, which is based on coarse quantization of oversampled (redundant) samples of a signal,(More)
—Sigma–delta modulation, a widely used method of analog-to-digital (A/D) signal conversion, is known to be robust to hardware imperfections, i.e., bit streams generated by slightly imprecise hardware components can be decoded comparably well. We formulate a model for robustness and give a rigorous analysis for single-loop sigma–delta modulation applied to(More)
Sigma-delta quantization is a method of representing bandlimited signals by 0−1 sequences that are computed from regularly spaced samples of these signals; as the sampling density λ → ∞, convolving these one-bit sequences with appropriately chosen kernels produces increasingly close approximations of the original signals. This method is widely used for(More)
We introduce a new architecture for pipelined (and also algorith-mic) A/D converters that give exponentially accurate conversion using inaccurate comparators. An error analysis of a sigma-delta converter with an imperfect comparator and a constant input reveals a self-correction property that is not inherited by the successive refinement quantization(More)
This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with &#x03B2; = &#x03C6; = (1 + &#x221A;5)/2, the golden ratio. It was previously shown that beta-encoders(More)
Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathematical model for the error analysis of the method measures the performance of a given scheme by the rate at which the associated reconstruction error decays as a function of the(More)
Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size δ is used to quantize m measurements y = Φx of a k-sparse signal x ∈ R N , where Φ satisfies the restricted isometry property, then the approximate(More)
In this paper we will describe a constructive method to find szlig-encodings (szlig-representations) with special properties. These include simultaneous szlig-encodings with respect to several bases and hybrid SigmaDelta/szlig-encodings. The main motivation for the latter scheme is to have bit representations whose robustness to additive circuit noise is(More)