Lowpass & Highpass Filter Characteristics 187 Another rare bird is the Halpern filter [23]. This is related to the Legendre­Papoulis filter in that it rolls off faster than a Butterworth but slower than a Chebyshev. Likewise, the Halpern filter has a monotonic passband without being maximally flat. The peak group delay near the cutoff is significantly lower than that of a Chebyshev filter but not as good as Butterworth or Legendre­Papoulis. I don't pretend that the information in this final section is going to be digestible to anyone without a quite advanced knowledge of mathematics, but do not fret. There is at present nothing to suggest that these filter types have anything to offer crossover design that is not already covered by the better-known filter types dealt with in detail above, so there seems no point in going further into the rather heavy mathematics required. References [1] Williams, Taylor, Electronic Filter Design Handbook, fourth ed., McGraw-Hill, USA, 2006, ISBN 0-07-147171-5. [2] van Valkenburg, Analog Filter Design, Holt-Saunders International Editions, 1982, ISBN 4-8338-0091-3. [3] H.M. Berlin, Design of Active Filters with Experiments, Blacksburg, VA, 1978, p. 85. [4] B. Hofer, Switch-mode amplifier performance measurements, Electronics World, USA, 2005, p. 30. [5] H. Bill, Precise active crossover, Electronics World, USA, 2009, p. 652.