Name
Abstract | ||
|---|---|---|
Sigma-delta modulation, a widely used method of analog-to-digital (A/D) signal conversion, is known to be robust to hardware imperfections, i.e., bit streams generated by slightly imprecise hardware components can be decoded comparably well. We formulate a model for robustness and give a rigorous analysis for single-loop sigma-delta modulation applied to constant signals (DC inputs) for N time cycles, with an arbitrary (small enough) initial condition uo, and a quantizer that may contain an offset error. The mean-square error (MSE) of any decoding scheme for this quantizer (with uo and the offset error known) is bounded below by 1/96N-3. We also determine the asymptotically best possible MSE as N→∞ for perfect decoding when uo=0 and uo=½. The robustness result is the upper bound that a triangular linear filter decoder (with both uo and the offset error unknown) achieves an MSE of 40/3N-3. These results establish the known result that the O(1/N3) decay of the MSE with N is optimal in the single-loop case, under weaker assumptions than previous analyses, and show that a suitable linear decoder is robust against offset error. These results are obtained using methods from number theory and Fourier analysis |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1109/18.930914 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
possible mse,sigma-delta modulation,known result,initial condition uo,fourier analysis,decoding scheme,n time cycle,single-loop sigma-delta modulation,hardware imperfection,mean-square error,error unknown,filtering,initial condition,delta sigma modulation,robustness,quantization,mse,decoding,upper bound,mean square error,linear filtering,sigma delta modulator,feedback,number theory,signal generators,signal analysis,quantizer,hardware | Topology,Discrete mathematics,Fourier analysis,Linear filter,Control theory,Upper and lower bounds,Modulation,Robustness (computer science),Decoding methods,Quantization (signal processing),Offset (computer science),Mathematics | Journal |
Volume | Issue | ISSN |
47 | 5 | 0018-9448 |
Citations | PageRank | References |
12 | 2.54 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. S. Gunturk | 1 | 36 | 5.37 |
| J. C. Lagarias | 2 | 563 | 235.61 |
| V. A. Vaishampayan | 3 | 909 | 87.62 |