Subject: Re: reverse engineering of acoustic sources From: Georg Essl <gessl(at)CS.PRINCETON.EDU> Date: Sat, 31 Jan 2004 14:07:56 -0500Hi Pierre, I do agree that inverse problems are hard. Though I would argue that the inverse spectral problem of the linear wave equation is much easier than the same for the articulatory tract, which is clearly not a as simple a situation. - Georg On Sat, 31 Jan 2004, Pierre Divenyi wrote: > Date: Sat, 31 Jan 2004 10:43:50 -0800 > From: Pierre Divenyi <pdivenyi(at)ebire.org> > To: Georg Essl <gessl(at)CS.Princeton.EDU>, AUDITORY(at)LISTS.MCGILL.CA > Subject: Re: reverse engineering of acoustic sources > > Pardon my bringing in a negative view, but I have serious doubts that a > unique solution to any specific wave can be found. Although I have never > delved into the mathematics of it, I only know of the problem in phonetics, > where the acoustic-to-articulatory inversion has been extensively > investigated, only to come up with the answer that solutions require very > restrictive initial and boundary values and functions. I can't imagine that > the acoustic-to-musical instrument problem should be any easier to solve. > But correct me if I am wrong. > > Pierre Divenyi > > At 01:13 PM 1/31/2004 -0500, Georg Essl wrote: > >Hi Jim, > > > > I think it's probably fair to say that the pure mathematicians who work > >on this don't necessarily have typical real-world acoustical situations in > >mind. The formalisms tend to isolate one problem and tend to try to make a > >dent there. So 2-D structures (membranes) and 3-D (rooms) cases are > >usually treated separately. > > > >As for excitations, these are usually not featured prominently, though > >they are definitely there implicitly at least. I'd say in the papers that > >I've read very often harmonic drivers (force-sustained) are assumed, but > >not necessarily. It helps to bring the wave equation into reduced > >Helmholtz form, which is convenient. It's a spatial problem only rather > >than a temporal and spatial problem that way. In other formalisms, the > >dynamic response in general usually with respect to the geometry of the > >situation is considered in which case asymptotic arguments pop up (often > >by lack of a better method). Asymptotic in this setting means that an > >approximate form is assumed whose error shrinks with some parameter > >becoming large, e.g. typically for high frequencies. Of course if the > >situations could be treated directly, one would. > > > >But despite all the simplications and reductions, the story isn't simple > >(and not fully understood), which is I guess the point I wanted to make > >with respect to the paragraph of the SciAm article. > > > >- Georg > > > >On Sat, 31 Jan 2004, beauchamp james w wrote: > > > > > Date: Sat, 31 Jan 2004 09:38:22 -0600 (CST) > > > From: beauchamp james w <jwbeauch(at)ux1.cso.uiuc.edu> > > > To: gessl(at)CS.Princeton.EDU > > > Cc: auditory(at)lists.mcgill.ca > > > Subject: Re: reverse engineering of acoustic sources > > > > > > Dear Georg, > > > > > > Thank you for your wonderful response to my question. > > > > > > I wonder if any of the mathematical solutions to this problem take > > > into account directivity and room responses and whether they work > > > for forced sustained vibrations (e.g., clarinet) as opposed to > > > free vibrations (e.g., a drum). > > > > > > Jim Beauchamp > > > > > >