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Stability Analysis of 1-Bit ΣΔ Modulators by Covering State Vector Transition with Hyper Cube for Specified Input Peak Amplitudes and Auto-Correlations
Mitsuhiko YAGYU Akinori NISHIHARA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2004/08/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Theory of Signals
stability, oversampling ΣΔ modulator, state vector transition, optimization,
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This paper presents an algorithm to analyze the stability and detect an upper-bound of every possible overload of a ΣΔ modulator for a set of input signals that are characterized by specified peak amplitudes and auto-correlations. The approach is to introduce a hyper cube in which all possible state vectors are recursively mapped into a subset of the hyper cube itself for the specified inputs and detect such a hyper cube by iteratively solving linear programming problems. Then the proposed algorithm may not identify every stable ΣΔ modulator but cannot evaluate any unstable ΣΔ modulator as a stable one. In numerical examples, two 1-bit ΣΔ modulators are analyzed, and it is revealed that a band-limitation of inputs to OSR 256 guarantees the rigorous stability even with an extension of input range to at least 240% of conventional range.