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Use of Frequency Overlap and Equalization to Produce High-Slope Linear-Phase Loudspeaker Crossover Networks
We have shown that linear-phase crossovers of high slope can be synthesized by subtracting a suitable low-pass output from a time-delayed version of the input signal. It would be nice to be able to avoid the expense of such an electronic time-delay network, however, and in the search for a means of doing so, we have subsequently shown that the introduction of an acoustic delay between the drivers cannot achieve the desired result. There is another possibility which suggests itself: gradually overlap the two halves of the crossover until the right half-plane zeros which are causing the non-minimum phase behavior migrate into the left half-phase and the system becomes minimum phase (but, of course, non flat). The higher the crossover order, the greater the overlap required and the greater the rippling in the combined output. Hence the usefulness of this technique for rendering the crossover minimum phase is essentially restricted to orders r<=3 in practice. Nevertheless it is of theoretical interest, for, once minimum-phase respnse is achieved, normal minimum-phase equalization will yield a flat, linear-phase crossover retaining the original high relative rolloff rates between the drivers. The equalization may be incorporated into a passive crossover network, or performed actively. This paper explores the overlap technique and shows how it affects crossovers of orders 1 through 4. It provides one more weapon in the rather sparsely equipped arsenal of transient-perfect actively.
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