Squared Chebyshev and Elliptic Crossovers

Sierra J. Squared Chebyshev and Elliptic Crossovers. In: AES Convention 155. Audio Engineering Society; 2023. Paper 181. Available from: https://aes.org/publications/elibrary-page/?id=22335

@inproceedings{Sierra2023_22335,
  author = {Sierra, Juan},
  title = {{Squared Chebyshev and Elliptic Crossovers}},
  booktitle = {AES Convention 155},
  note = {Paper 181},
  year = {2023},
  month = oct,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=22335}
}

TY  - CPAPER
TI  - Squared Chebyshev and Elliptic Crossovers
AU  - Sierra, Juan
T2  - AES Convention 155
M1  - Paper 181
PY  - 2023
DA  - 2023/10/06
UR  - https://aes.org/publications/elibrary-page/?id=22335
PB  - Audio Engineering Society
LA  - en
AB  - Squared Butterworth crossovers, also known as Linkwitz-Riley crossovers, have found extensive use in audio ap-plications for splitting a spectrum into multiple segments. However, for applications involving low-pass and high-pass filters, alternative options like Chebyshev (Type-I and II) and elliptic filters often offer advantages. Squared Chebyshev and elliptic crossovers have garnered less attention, primarily due to the absence of closed-form ex-pressions, owing to their mathematical complexity. This paper introduces closed-form expressions, accompanied by explicit constraints for achieving perfect magnitude reconstruction in these crossovers. Furthermore, as these crossovers are all-pass equivalent, they can serve as fundamental components for constructing more intricate filter structures, including shelving, parametric, and notch filters based on Chebyshev and elliptic designs.
ER  -