Image Processing Reference
In-Depth Information
And the second derivative is
2
q
f (x)
q
x
2
¼
q
(Ax þ b)
q
x
¼ A
3.12.3 D
ERIVATIVE OF A
V
ECTOR
F
UNCTION WITH
R
ESPECT TO A
V
ECTOR
Let f
(
x
) 2
R
m
be a vector function of vector x
2
R
n
, then by de
nition
2
4
3
5
q
f
1
(
x
)
q
x
1
q
f
2
(
x
)
q
x
1
q
f
m
(
x
)
q
x
1
q
f
1
(
x
)
q
x
2
q
f
2
(
x
)
q
x
2
q
f
m
(
x
)
q
x
2
q
f
(
x
)
q
x
¼
(
3
:
215
)
.
.
.
.
q
f
1
(
x
)
q
x
n
q
f
2
(
x
)
q
x
n
q
f
m
(
x
)
q
x
n
Example 3.55
, then
x
1
x
2
þ
3x
2
þ
4x
3
5
Let x 2 R
3
and f (x)
¼
x
1
x
2
þ x
2
2x
1
x
2
x
3
2
4
3
5
q
f
1
(x)
q
x
1
q
f
2
(x)
q
x
1
2
4
3
5
2x
1
x
2
x
2
2x
2
x
3
q
f (x)
q
x
¼
q
f
1
(x)
q
x
2
q
f
2
(x)
q
x
2
x
1
þ
¼
3 x
1
2x
1
x
3
þ
1
4
2x
1
x
2
q
f
1
(x)
q
x
3
q
f
2
(x)
q
x
3
PROBLEMS
3.1
(a) Let
x
(
n
) ¼ d(
n
) þ
d(
n
) þ
d(
n
)
and
2
1
3
2
h
(
n
) ¼ d(
n
) þ d(
n
1
) þ
2
d(
n
2
)
.
(b) Consider the LTI system with impulse response
Find x
(
n
)
*
h
(
n
)
2
n
u
(
n
)
h
(
n
) ¼
1
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