Graphics Reference
In-Depth Information
Table 19.1:
Filters and their Fourier transforms.
Comments
y
=
f
x
y
=
f
(
)
F
(
)(
v
)
1
1
0
0
The unit box filter;
transform is sinc.
−
3
−
2
−
1
0
1
23
−
3
−
2
−
1
0
1
2
3
1
1
The sinc filter with
spacing one;
transform is the
unit box.
0
0
−
3
−
2
−
1
0
1
23
−
3
−
2
−
1
0
1
2
3
1
1
The Gaussian filter.
Transforms to a scaled
Gau
ss
ian. Shown is
0
0
g
(
√
π
x
)
, which
transforms to itself.
−
3
−
2
−
1
0
1
2
3
−
3
−
2
−
1
0
1
2
3
1
1
The cubic B-spline
filter. Fairly
band-limited, but
attenuates signals
except near
0
0
=
0.
v
−
3
−
2
−
1
0
1
2
3
−
3
−
2
−
1
0
1
2
3
The Catmull-Rom
filter. Less
band-limited, but
better signal
preservation near
v
1
1
0
0
=
0.
−
3
−
2
−
1
0
1
2
3
−
3
−
2
−
1
0
1
2
3
1
1
Mitchell-Netravali. A
compromise between
the B-spline and the
Catmull-Rom filters.
0
0
−
3
−
2
−
1
0
1
2
3
−
3
−
2
−
1
0
1
2
3
