Stochastic analysis of the /spl Sigma//spl Delta/ modulator and differential pulse code modulator
作者： R. Sharma , I.A. Bucklew , W.A. Sethares
DOI: 10.1109/82.633434
关键词: Stochastic process 、 Gaussian process 、 Mathematics 、 Delta modulation 、 Adaptive algorithm 、 Pulse-code modulation 、 Sigma 、 Control theory 、 Topology 、 Dither 、 Adaptive filter
摘要: One of the most popular systems for performing high resolution analog to digital conversion is /spl Sigma//spl Delta/ modulator. Though common in applications, theoretical analysis modulator difficult due presence a discontinuous quantizer This paper presents asymptotic results regarding statistical behavior when inside loop dithering utilized. In some recent papers examining stochastic Delta/, it was shown (via simulations) that input can be accurately modeled as stationary Gaussian process. Our shows both and quantization noise are asymptotically processes, under mild assumptions on dither The this derived by letting stepsize approach zero, analytical related adaptive filtering algorithms. valid large collection signals, including ARMA processes. Furthermore, previous assumed never overloaded, while present does not make assumption. It also Differential Pulse Code Modulator fact analogous Simulation presented first-order two second-order modulators demonstrate practicality analysis.
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