DocumentCode :
464065
Title :
Formal Spectral Theory for Ideal Sigma-Delta Quantization with Stationary Time-Varying Inputs
Author :
Thao, N.T.
Author_Institution :
Dept. of Electr. Eng., CUNY, New York, NY, USA
Volume :
3
fYear :
2007
fDate :
15-20 April 2007
Abstract :
Because a ΣΔ modulator is a nonlinear feedback system, its rigorous signal analysis escapes from the standard theories used in signal processing and communications. We introduce mathematical tools that are new to these two areas and that lead to systematic and high-level methods for the spectral error analysis of ΣΔ modulators. They include the use of dynamical system techniques, of the roots of ergodic theory and the spectral properties of unitary operators in a Hubert space. In this paper, we show their application to the case of ideal ΣΔ modulation, thus providing a formal and concise theory for the extensive derivations performed by Gray et al. and He et al. in this special case some 15 years ago. We finally point to the potential extension of these new methods to a substantially larger class of ΣΔ modulators.
Keywords :
error analysis; feedback; quantisation (signal); sigma-delta modulation; signal processing; spectral analysis; ΣΔ modulator; Hubert space; ergodic theory; formal spectral theory; ideal sigma-delta quantization; nonlinear feedback system; rigorous signal analysis; spectral error analysis; stationary time-varying inputs; Delta-sigma modulation; Difference equations; Error analysis; Feedback; Helium; Nonlinear equations; Quantization; Signal analysis; Signal processing; Spectral analysis; Sigma-Delta modulation; error analysis; feedback systems; nonlinear systems; spectral analysis;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on
Conference_Location :
Honolulu, HI
ISSN :
1520-6149
Print_ISBN :
1-4244-0727-3
Type :
conf
DOI :
10.1109/ICASSP.2007.367128
Filename :
4218001
Link To Document :
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