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Linkwitz–Riley filter
A Linkwitz–Riley (L-R) filter is an infinite impulse response filter used in Linkwitz–Riley audio crossovers, named after its inventors Siegfried Linkwitz and Russ Riley, which was originally described in ''Active Crossover Networks for Noncoincident Drivers'' in (JAES Volume 24 Issue 1 pp. 2-8; February 1976 ). It is also known as a ''Butterworth squared'' filter. An L-R crossover consists of a parallel combination of a low-pass and a high-pass L-R filter. The filters are usually designed by cascading two Butterworth filters, each of which has −3 dB gain at the cut-off frequency. The resulting Linkwitz–Riley filter has a −6 dB gain at the cutoff frequency. This means that summing the low-pass and high-pass outputs, the gain at the crossover frequency will be 0 dB, so the crossover behaves like an all-pass filter, having a flat amplitude response with a smoothly changing phase response. This is the biggest advantage of L-R crossovers compared to Butterworth crossovers, whose summed output has a +3 dB peak around the crossover frequency. Since cascading two nth order Butterworth filters will give a 2nth order Linkwitz–Riley filter, theoretically any 2nth order Linkwitz–Riley crossover can be designed. However, crossovers of higher order than 4th may have less usability due to their increasing peak in group delay around crossover frequency and complexity.
==Common types==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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