Crossover networks for multi-way loudspeaker systems and audio processing are reviewed, including both analog and digital designs.Ahigh-quality crossover network must maintain a flat overall magnitude response, within small tolerances, and a sufficiently linear phase response. Simultaneously, the crossover filters for each band must provide a steep transition to properly separate the bands, also accounting for the frequency ranges of the drivers. Furthermore, crossover filters affect the polar response of the loudspeaker, which should vary smoothly and symmetrically in the listening window. The crossover filters should additionally be economical to implement and not cause much latency. Perceptual aspects and the inclusion of equalization in the crossover network are discussed. Various applications of crossover filters in audio engineering are explained, such as in multiband compressors and in effects processing. Several methods are compared in terms of the basic requirements and computational cost. The results lead to the recommendation of an all-pass-filter--based Linkwitz-Riley crossover network, when a computationally efficient minimum-phase solution is desired. When a linear-phase crossover network is selected, the throughput delay becomes larger than with minimum-phase filters. Digital linear-phase crossover filters having a finite impulse response may be designed by optimization and implemented efficiently using a complementary structure.
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