Biot–Tolstoy–Medwin diffraction model

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.[1]

Impulse response

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The impulse response according to BTM is given as follows:[2]

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

 

See also

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Notes

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  1. ^ Calamia 2007, p. 182.
  2. ^ Calamia 2007, p. 183.

References

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  • 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.