Optimum "L" filter

The Optimum "L" filter (also known as a Legendre–Papoulis filter) was proposed by Athanasios Papoulis in 1958. It has the maximum roll off rate for a given filter order while maintaining a monotonic frequency response. It provides a compromise between the Butterworth filter which is monotonic but has a slower roll off and the Chebyshev filter which has a faster roll off but has ripple in either the pass band or stop band. The filter design is based on Legendre polynomials which is the reason for its alternate name and the "L" in Optimum "L".

See also


  • Athanasios Papoulis (1958). Optimum Filters with Monotonic Response. Proceedings to the IRE.
  • Kuo, Franklin F. (1966). Network Analysis and Synthesis. Wiley. ISBN 0-471-51118-8. Second Edition.
  • Optimum “L” Filters: Polynomials, Poles and Circuit Elements by C. Bond, 2004
  • Notes on “L” (Optimal) Filters by C. Bond, 2011

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