Stability Analysis of 1-Bit ΣΔ Modulators by Covering State Vector Transition with Hyper Cube for Specified Input Peak Amplitudes and Auto-Correlations(Theory of Signals)(<Special Section>Digital Signal Processing)

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概要

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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.

• 社団法人電子情報通信学会の論文
• 2004-08-01

著者

• NISHIHARA Akinori

  the Center for Research and Development of Educational Technology, Tokyo Institute of Technology

• Yagyu Mitsuhiko

  The Department Of Electrical And Electronic Engineering School Of Science And Technology Meiji Unive

• Nishihara Akinori

  The Center For Research And Development Of Educational Technology Tokyo Institute Of Technology

関連論文

• Minimization of Output Errors of FIR Digital Filters by Multiple Decompositions of Signal Word
• Stability Analysis of 1-Bit ΣΔ Modulators by Covering State Vector Transition with Hyper Cube for Specified Input Peak Amplitudes and Auto-Correlations(Theory of Signals)(Digital Signal Processing)

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