In applied mathematics, the Biot–Tolstoy–Medwin (BTM) diffraction model describes edge diffraction. Unlike the uniform theory of diffraction (UTD), BTM does not make the high frequency assumption (in which edge lengths and distances from source and receiver are much larger than the wavelength). BTM sees use in acoustic simulations.Calamia 2007, p. 182.
Impulse response
The impulse response according to BTM is given as follows:Calamia 2007, p. 183.
The general expression for sound pressure is given by the convolution integral
where represents the source signal, and represents the impulse response at the receiver position. The BTM gives the latter in terms of
the source position in cylindrical coordinates where the -axis is considered to lie on the edge and is measured from one of the faces of the wedge. the receiver position the (outer) wedge angle and from this the wedge index the speed of sound
as an integral over edge positions
where the summation is over the four possible choices of the two signs, and are the distances from the point to the source and receiver respectively, and is the Dirac delta function.
where
Notes
References Calamia, Paul T. and Svensson, U. Peter, "Fast time-domain edge-diffraction calculations for interactive acoustic simulations," EURASIP Journal on Advances in Signal Processing, Volume 2007, Article ID 63560. American Institute of Physics (AIP) Information about Herman (Hank) Medwin (1920–2006) A tribute to Hank Medwin at ResearchGate Herman Medwin ● 1920–2006 at the Journal of the Acoustical Society of America (JASA) website