They Exist: Limit Cycles in High Order Sigma Delta Modulators

Reiss JD, Sandler MB. They Exist: Limit Cycles in High Order Sigma Delta Modulators. In: AES Convention 114. Audio Engineering Society; 2003. Paper 5832. Available from: https://aes.org/publications/elibrary-page/?id=12491

@inproceedings{Reiss2003_12491,
  author = {Reiss, Joshua D. and Sandler, Mark B.},
  title = {{They Exist: Limit Cycles in High Order Sigma Delta Modulators}},
  booktitle = {AES Convention 114},
  note = {Paper 5832},
  year = {2003},
  month = mar,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=12491}
}

TY  - CPAPER
TI  - They Exist: Limit Cycles in High Order Sigma Delta Modulators
AU  - Reiss, Joshua D.
AU  - Sandler, Mark B.
T2  - AES Convention 114
M1  - Paper 5832
PY  - 2003
DA  - 2003/03/06
UR  - https://aes.org/publications/elibrary-page/?id=12491
PB  - Audio Engineering Society
LA  - en
AB  - A compact form can be used to describe an arbitrary high order sigma delta modulator. Such a format is beneficial because it provides insight into the structure of limit cycles in sigma delta modulators. We consider modulators of any order with periodic output. We make no assumptions regarding the input and are thus able to prove necessary conditions for limit cycles in the output. We show that the input must be periodic, but may have a different period from both integrator output and quantised output. We derive what this implies regarding limit cycles for sinusoidal inputs. Finally, we give examples where sinusoidal input to a third order modulator results in a limit cycle of a different frequency.
ER  -