Estimation of Initial States of Sigma-delta Modulators

Ho C, Ling BWK, Reiss JD. Estimation of Initial States of Sigma-delta Modulators. In: AES Convention 120. Audio Engineering Society; 2006. Paper 6698. Available from: https://aes.org/publications/elibrary-page/?id=13502

@inproceedings{Ho2006_13502,
  author = {Ho, Charlotte and Ling, Bingo Wing-Kuen and Reiss, Joshua D.},
  title = {{Estimation of Initial States of Sigma-delta Modulators}},
  booktitle = {AES Convention 120},
  note = {Paper 6698},
  year = {2006},
  month = may,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=13502}
}

TY  - CPAPER
TI  - Estimation of Initial States of Sigma-delta Modulators
AU  - Ho, Charlotte
AU  - Ling, Bingo Wing-Kuen
AU  - Reiss, Joshua D.
T2  - AES Convention 120
M1  - Paper 6698
PY  - 2006
DA  - 2006/05/06
UR  - https://aes.org/publications/elibrary-page/?id=13502
PB  - Audio Engineering Society
LA  - en
AB  - In this paper, an initial condition of a sigma-delta modulator is estimated based on quantizer output bit streams and an input signal. The set of initial conditions that generate a stable trajectory is characterized. It is found that this set, as well as the set of initial conditions corresponding to the quantizer output bit streams, are convex. Also, it is found that the mapping from the set of initial conditions to the stable admissible set of quantizer output bit streams is invertible if the loop filter is unstable. Hence, the initial condition corresponding to given stable admissible quantizer output streams and an input signal is uniquely defined when the loop filter is unstable, and a projection onto convex set approach is employed for approximating the initial condition.
ER  -