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.
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https://aes2.org/publications/elibrary-page/?id=22335
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