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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
679:{\displaystyle h(\tau )=-{\frac {\nu }{4\pi }}\sum _{\phi _{i}=\pi \pm \theta _{S}\pm \theta _{R}}\int _{z_{1}}^{z_{2}}\delta \left(\tau -{\frac {m+l}{c}}\right){\frac {\beta _{i}}{ml}}\,dz}
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assumption (in which edge lengths and distances from source and receiver are much larger than the wavelength). BTM sees use in acoustic simulations.
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represents the impulse response at the receiver position. The BTM gives the latter in terms of
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878:{\displaystyle \beta _{i}={\frac {\sin(\nu \phi _{i})}{\cosh(\nu \eta )-\cos(\nu \phi _{i})}}}
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1004:{\displaystyle \eta =\cosh ^{-1}{\frac {ml+(z-z_{S})(z-z_{R})}{r_{S}r_{R}}}}
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where the summation is over the four possible choices of the two signs,
142:{\displaystyle p(t)=\int _{0}^{\infty }h(\tau )q(t-\tau )\,d\tau }
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313:is measured from one of the faces of the wedge.
214:the source position in cylindrical coordinates
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749:to the source and receiver respectively, and
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293:-axis is considered to lie on the edge and
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368:{\displaystyle (r_{R},\theta _{R},z_{R})}
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266:{\displaystyle (r_{S},\theta _{S},z_{S})}
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25:–Tolstoy–Medwin (BTM) diffraction model
51:according to BTM is given as follows:
438:{\displaystyle \nu =\pi /\theta _{W}}
7:
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470:as an integral over edge positions
181:represents the source signal, and
97:
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729:are the distances from the point
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404:and from this the wedge index
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1021:Uniform theory of diffraction
35:(UTD), BTM does not make the
33:uniform theory of diffraction
1089:. You can help Knowledge by
397:{\displaystyle \theta _{W}}
54:The general expression for
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377:the (outer) wedge angle
1141:Signal processing stubs
762:{\displaystyle \delta }
306:{\displaystyle \theta }
1085:-related article is a
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316:the receiver position
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1048:Calamia 2007, p. 183.
1039:Calamia 2007, p. 182.
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771:Dirac delta function
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203:{\displaystyle h(t)}
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447:the speed of sound
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18:applied mathematics
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1136:Signal processing
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1083:signal processing
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742:{\displaystyle z}
722:{\displaystyle l}
702:{\displaystyle m}
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483:{\displaystyle z}
460:{\displaystyle c}
286:{\displaystyle z}
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58:is given by the
49:impulse response
43:Impulse response
29:edge diffraction
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56:sound pressure
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37:high frequency
31:. Unlike the
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1091:expanding it
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469:
151:
53:
46:
21:
15:
60:convolution
1130:Categories
1056:References
273:where the
27:describes
961:−
939:−
918:
910:−
899:η
861:ϕ
857:ν
851:
845:−
839:η
836:ν
830:
813:ϕ
809:ν
803:
785:β
757:δ
651:β
622:−
619:τ
611:δ
583:∫
571:θ
567:±
558:θ
554:±
551:π
539:ϕ
534:∑
527:π
520:ν
515:−
506:τ
427:θ
418:π
412:ν
386:θ
341:θ
301:θ
239:θ
137:τ
127:τ
124:−
109:τ
98:∞
89:∫
62:integral
1015:See also
769:is the
1062:63560.
888:where
152:where
20:, the
1081:This
1027:Notes
1087:stub
906:cosh
827:cosh
709:and
47:The
23:Biot
848:cos
800:sin
16:In
1132::
773:.
1118:e
1111:t
1104:v
1093:.
994:R
990:r
984:S
980:r
974:)
969:R
965:z
958:z
955:(
952:)
947:S
943:z
936:z
933:(
930:+
927:l
924:m
913:1
902:=
870:)
865:i
854:(
842:)
833:(
822:)
817:i
806:(
794:=
789:i
737:z
717:l
697:m
674:z
671:d
664:l
661:m
655:i
644:)
638:c
634:l
631:+
628:m
615:(
604:2
600:z
592:1
588:z
575:R
562:S
548:=
543:i
524:4
512:=
509:)
503:(
500:h
478:z
455:c
431:W
422:/
415:=
390:W
363:)
358:R
354:z
350:,
345:R
337:,
332:R
328:r
324:(
281:z
261:)
256:S
252:z
248:,
243:S
235:,
230:S
226:r
222:(
198:)
195:t
192:(
189:h
169:)
166:t
163:(
160:q
134:d
130:)
121:t
118:(
115:q
112:)
106:(
103:h
93:0
85:=
82:)
79:t
76:(
73:p
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