Digital Signal Processing Reference
In-Depth Information
FIGURE 6.1
16
×
16 pixel image of the letter E.
⎡
f
(, )
00
f
(,)
01
…
f
(,
0
N
−
1
)
⎤
2
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
f
(, )
10
f
(, )
11
…
f
(,
1
N
−
1
)
2
.
(6.1)
f=
.
.
fN
(
−
10
,
)
fN
(
−
11
, )
…
ffN
(
−
1
,
N
−
1
)
⎣
⎦
1
1
1
2
Each element of the matrix
f
can also be termed a
pixel
, giving a total of
N
pixels in the entire image. Some common examples of two-dimen-
sional discrete signals are:
at
N
1
2
•
2-d impulse function
⎧
1
,
for
nn
==
0
⎪
⎪
1
2
(6.2)
δ
(, )
nn
=
12
0
,
otherwise
•
2-d unit step function
⎧
1
,
for
nn
≥
0
,
≥
0
⎪
⎪
1
2
(6.3)
un n
(, )
=
12
0
,
otherwise
Two-dimensional discrete systems
A system with two-dimensional discrete space input and output signals is
termed a 2
-d discrete-space system
, as shown in
Figure 6.2
.
The relationship
between the output and input of a 2-d discrete system is given by
