A complete series of all-pass crossover functions is derived. These functions are useful in the design of crossover systems for audio equipment such as loudspeakers and signal processors. The series include the known all-pass crossover functions as well as many new designs. A common property of functions in the series is that their singularities are positioned upon a circle in the complex-frequency plane. Such functions are particularly suitable for audio applications. Response characteristics are given for all-pass crossover systems up to ninth order, and the importance of a systems approach to crossover-network design is emphasized.
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