744-745 / 2239
Convolution integral
C-S Chui and R Mohan, Med Phy 15(2), 1988
A convolution is an integral that
expresses
the amount of
overlap of one function as it
is shifted over another
function
.
step function
1D kernel function
The steps to convolve these two functions are:
1.
Folding
2.
Displacement
3.
Multiplication
4.
Integration
[
]
( )
(
) (
)
∫ ∫
∞
∞−
∞
∞−
− −
=
⊗
'
'
'
,'
' ,'
,
dy dx y yx xgyxf
yxg f
2D definition