Optimum "L" filter

Linear analog electronic filters
Network synthesis filters Butterworth filter Chebyshev filter Elliptic (Cauer) filter Bessel filter Gaussian filter Optimum "L" (Legendre) filter Linkwitz–Riley filter
Image impedance filters Constant k filter m-derived filter General image filters Zobel network (constant R) filter Lattice filter (all-pass) Bridged T delay equaliser (all-pass) Composite image filter mm'-type filter
Simple filters RC filter RL filter LC filter RLC filter

Comparison of filter magnitude between Butterworth-, Legendre- and Chebyshev-Type1-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".

References

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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Optimum "L" filter

See also

References