Audio Engineering Society
نویسنده
چکیده
One of the greatest unsolved problems in the theory of sigma delta modulation concerns the ability to analytically derive the stability, or boundedness, of a high order sigma delta modulator (SDM). In this work, we describe the existing literature and try to clarify the issues involved. We fully derive the stability of first order sigma delta modulators, and derive some important results for the basic second order sigma delta modulator. For third order sigma delta modulators, we describe interesting simulated results as well as sketch a proof of instability, based on linear programming, for one particular SDM. Finally, we present two theoretical results concerning stability of general high order SDMs that point towards promising directions of future research. Our goal is to derive an analytical method of determining the stability of sigma delta modulators. That is, we wish to present a mathematical framework, based on state space modeling and symbolic dynamics, for deriving the stability of 1-bit Sigma Delta Modulators (SDMs). We will focus on DC inputs, since this represents the most relevant (and easiest) practical condition. We wish to determine the maximum value of the constant applied input which will produce stable output indefinitely.
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This convention paper has been reproduced from the author's advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42 Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Rep...
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This convention paper has been reproduced from the author’s advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42nd Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. R...
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