Multistage sigma-delta modulation

A theoretical basis is provided for multistage sigma-delta modulation (MSM), which is a cascade realization of several single-loop sigma-delta modulators with a linear combinatorial network. Equations are derived describing the output and the quantization noise of MSM for an arbitrary input signal, and the noise-shaping characteristic of MSM is investigated. The spectral characteristics of an m-stage sigma-delta modulator with both DC and sinusoidal inputs are developed. For both types of inputs the binary quantizer noise of the mth (m>or=3) quantizer, which appears at the output as an mth order difference, is asymptotically white, uniformly distributed, and uncorrelated with the input level. It is also found that for an m-stage sigma-delta quantizer with either an ideal low-pass filter or a sinc/sup m+1/ filter decoder, the average quantization noise of the system is inversely proportional to the (2m+1)th power of the oversampling ratio. This implies that the high-order systems are favourable in terms of the trade-off between the quantization noise and oversampling ratio. Simulation results are presented to support the theoretical analysis. >

[1]  Robert M. Gray,et al.  Two-stage sigma-delta modulation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  Robert M. Gray,et al.  Spectral analysis of quantization noise in a single-loop sigma-delta modulator with DC input , 1989, IEEE Trans. Commun..

[3]  James C. Candy,et al.  A Use of Limit Cycle Oscillations to Obtain Robust Analog-to-Digital Converters , 1974, IEEE Trans. Commun..

[4]  Wu Chou,et al.  Quantization noise in single-loop sigma-delta modulation with sinusoidal inputs , 1989, IEEE Trans. Commun..

[5]  Hiroshi Inose,et al.  A unity bit coding method by negative feedback , 1963 .

[6]  H. Inose,et al.  A Telemetering System by Code Modulation - Δ- ΣModulation , 1962, IRE Transactions on Space Electronics and Telemetry.

[7]  Atsushi Iwata,et al.  Oversampling A-to-D and D-to-A converters with multistage noise shaping modulators , 1988, IEEE Trans. Acoust. Speech Signal Process..

[8]  Toshio Hayashi,et al.  A multistage delta-sigma modulator without double integration loop , 1986, 1986 IEEE International Solid-State Circuits Conference. Digest of Technical Papers.

[9]  F. Hahn,et al.  On Affine Transformations of Compact Abelian Groups , 1963 .

[10]  J. Candy,et al.  The Structure of Quantization Noise from Sigma-Delta Modulation , 1981 .

[11]  A. Postnikov,et al.  Ergodic Problems in the Theory of Congruences and of Diophantine Approximations , 1967 .

[12]  James C. Candy,et al.  Using Triangularly Weighted Interpolation to Get 13-Bit PCM from a Sigma-Delta Modulator , 1976, IEEE Trans. Commun..

[13]  F. J. Hahn.  Errata: Affine Transformations of Compact Abelian Groups , 1964 .

[14]  James C. Candy,et al.  Decimation for Sigma Delta Modulation , 1986, IEEE Trans. Commun..

[15]  A. Nuttall.  Some windows with very good sidelobe behavior , 1981 .

[16]  James C. Candy,et al.  A Use of Double Integration in Sigma Delta Modulation , 1985, IEEE Trans. Commun..

[17]  H. Weyl.  Über die Gleichverteilung von Zahlen mod. Eins , 1916 .

[18]  Robert M. Gray,et al.  Oversampled Sigma-Delta Modulation , 1987, IEEE Trans. Commun..