Abstract
A description is given of the output of most linear systems in terms of certain properties of the system's impulse response function and of the input signal. The description is particularly simplified when the input signal has a small fractional bandwidth; furthermore, this simplified description, although based on the supposition of a small fractional bandwidth, is shown numerically to apply well even when the fractional bandwidth is as large as unity. The author's “Image Pulse” theory of acoustic echo formation and “Replica Pulse” theory of acoustic radiation are demonstrated to be particular cases of the small fractional bandwidth version of the above more general linear system theory. Examples are provided showing the very good agreement between radiated waveforms obtained by using the band limited formulae of the Replica Pulse theory and the non-band limited formulae of the linear system theory, even when employing input pulses of only a few cycles duration.
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