Biot–Tolstoy–Medwin diffraction model
In applied mathematics, the Biot–Tolstoy–Medwin diffraction model describes edge diffraction. Unlike the uniform theory of diffraction, BTM does not make the high frequency assumption. BTM sees use in acoustic simulations.
Impulse response
The impulse response according to BTM is given as follows: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 wedge angle and from this the wedge index
- the speed of sound
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