Sparse sampling of signal innovations

Sparse sampling of continuous-time sparse signals is addressed. In particular, it is shown that sampling at the rate of innovation is possible, in some sense applying Occam's razor to the sampling of sparse signals. The noisy case is analyzed and solved, proposing methods reaching the optimal performance given by the Cramer-Rao bounds. Finally, a number of applications have been discussed where sparsity can be taken advantage of. The comprehensive coverage given in this article should lead to further research in sparse sampling, as well as new applications. One main application to use the theory presented in this article is ultra-wide band (UWB) communications

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

is paper deals with the deterministic analysis of oversampled A/D conversion (ADC), the properties derivable from such an analysis, and the consequences on reconstruc- tion using nonlinear decoding. Given a bandlimited input X producing a quantized version C , we consider the set of all input signals that are bandlimited and produce C. We call any element of this set a consistent estimate of X. Regardless of the type of encoder (simple, predictive, or noise-shaping), we show that this set is convex, and as a consequence, any nonconsistent estimate can be improved. We also show that the classical linear decoding estimates are not necessarily consistent. Numerical tests performed on simple ADC, single-loop, and multiloop ΣΔ modulation show that consistent estimates yield an MSE that decreases asymptotically with the oversampling ratio faster than the linear decoding MSE by approximately 3 dB/octave. This implies an asym totic MSE of the order of O(R-('"+')) instead of O(R-(2"c'p)in linear decoding, where R is the oversampling ratio and n the order of the modulator. Methods of improvements of nonconsistent estimates based on the deterministic knowledge of the quantized signal are proposed for simple ADC, predictive ADC, single-loop, and multiloop ΣΔ modulation

Lower Bound on the Mean-Squared Error in Oversampled Quantization of Periodic Signals Using Vector Quantization Analysis

Oversampled analog-to-digital conversion is a technique which permits high conversion resolution using coarse quantization. Classically, by lowpass filtering the quantized oversampled signal, it is possible to reduce the quantization error power in proportion to the oversampling ratio R. In other words, the reconstruction mean-squared error (MSE) is i