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Convolution
03/01/13
This is an integral transform of with as the kernel function
If the kernel is invariant, such that , the transform
becomes a convolution, and (following the convolution theorem)
In general, however, the kernel varies with position, due to divergence,
changes in energy, and the heterogeneity of the medium
Ԧ =ම Ԧ Ԧ , Ԧ
Ԧ , Ԧ = Ԧ − Ԧ
Ԧ = Ԧ ∗ Ԧ , Ԧ =
−1
( ) ⋅
( )
Ԧ , Ԧ
T
Ԧ