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- W2080931804 abstract "We establish an optical analogy for the processing of spherical wavefronts in conical bore segments. A reentrant discontinuity acts like a converging lens or mirror to give outgoing waves a more positive vergence than incoming waves [M.P. Keating, Am. J. Phys. 43, 766–769 (1975)]. Impulse responses for single interactions with such a discontinuity include exponentially growing wakes, which become unmanageable very quickly in digital convolutions. Geometrical considerations rule out a reentrant discontinuity existing in isolation, and its troublesome behavior is kept under control by multiple reflections involving another discontinuity of stronger, negative power. In closed systems this process shows a “sorcerer's apprentice” type of behavior, in which a temporary solution to the problem turns into the problem for the next cycle. Fortunately that problem becomes more deltalike as time progresses, and there is a tendency for it to be cancelled by a neighboring delta. In open systems the behavior is much tamer, with the extended response dying out very quickly. Our piecewise analytic results suggest some approximations which may be useful in digital convolutions." @default.
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- W2080931804 date "1986-12-01" @default.
- W2080931804 modified "2023-09-26" @default.
- W2080931804 title "Impulse responses for reentrant discontinuities in bores" @default.
- W2080931804 doi "https://doi.org/10.1121/1.2024017" @default.
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