On the reflection functions associated with discontinuities in conical bores

Abstract

The decomposition of reflections by finite tubes into successive elementary reflections by the input, discontinuities, and output of the tubes is interesting for its physical reasoning and for calculations using multiconvolution. In the case of tubes with conical bores, Martinez and Agulló [J. Martinez and J. Agulló, J. Acoust. Soc. Am. 84, 1613–1619 (1988)] have stated that in certain cases, the elementary reflection functions can be growing (causal) exponentials. Although such functions do not have Fourier transforms, Agulló et al. have assumed that they are inverse Fourier transforms of functions of frequency. It is shown that this assumption is erroneous. but by using a Laplace transform (i.e., by introducing losses through a complex frequency), we have also shown that for a general class of physically feasible systems, the decomposition into growing exponentials is valid.