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Multiresolution Speaker Systems

We are all familiar with speaker cabinets containing woofers, midrange, and tweeters, etc. Each cabinet can be considered a monaural multiresolution speaker system, typically three-way. Additionally there is often a subwoofer somewhere putting out the deep bass.

The Kenwood JL-840W speaker systems are four-way:23They use four circular drivers having diameters 30, 12, 6, and 3 cm.24 The crossover frequencies are at 2, 5, and 10 kHz, which is at $ ka = 5.5$ for the speaker driving below crossover, where $ k$ is wave number in radians per meter, as usual, and $ a$ is speaker radius.25 The nominal total frequency range of the system is 20-20 kHz, but amplitude drops off in the woofer (30 cm) for wavelengths much greater than the diameter, which must be compensated by extra drive. The super-tweeter, tweeter, and midrange drivers have diameters on the order of one to two wavelengths. The woofer high-end is near that range, but must handle all lower frequencies as well.

We can extend existing $ N$ -way speaker systems to multiresolution line arrays in a straightforward manner. We use the term Huygens Array (HA) to refer to any collection of drivers used as a spatial imaging array, and in particular, Huygens Octave Panels (HOP) will refer to multiresolution line arrays having octave divisions.26

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``A Spatial Sampling Approach to Wave Field Synthesis: PBAP and Huygens Arrays'', by Julius O. Smith III, Published 2019-11-18:
Copyright © 2020-05-15 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University