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Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)
Pacific Grove, CA, USA
Oct. 31, 1994 to Nov. 2, 1994
ISSN: 1058-6393
ISBN: 0-8186-6405-3
pp: 1536-1540
N.T. Thao , Dept. of Electr. & Electron. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong
M. Vetterli , Dept. of Electr. & Electron. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong
ABSTRACT
Research has been devoted to optimal signal reconstruction by /spl Sigma//spl Delta/ modulation. Using classical linear filtering, the reconstruction mean squared error (MSE) asymptotically decreases with the oversampling ratio R by R/sup -(2n+1)/, where n is the order of the modulator. Using a nonlinear reconstruction scheme, an improvement of the MSE asymptotic behavior by 3 dB per octave of R has been observed for time-varying, periodic and bandlimited input signals. This implies an MSE of /spl Oscr/(R/sup -(2n+2)/). We show for the multi-loop configuration of the /spl Sigma//spl Delta/ modulation and with the same kind of input signals that the asymptotic behavior of the reconstruction MSE cannot be less than /spl Oscr/(R/sup -(2n+2)/), including optimal reconstruction.<>
INDEX TERMS
signal reconstruction, sigma-delta modulation, filtering theory, signal sampling, error analysis
CITATION

N. Thao and M. Vetterli, "Lower bound on the mean squared error in multi-loop /spl Sigma//spl Delta/ modulation with periodic bandlimited signals," Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers(ACSSC), Pacific Grove, CA, USA, 1995, pp. 1536-1540.
doi:10.1109/ACSSC.1994.471715
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