Image Processing Reference
In-Depth Information
Using z-transform,
nd the response y
(
n
)
of this system to the input
4
n
u
(
n
)
1
x
(
n
) ¼
3.2
Determine the ROCs and z-transforms of each of the following sequences:
(a) x
(
n
) ¼ (
n
u
(
n
) þ
2
n
u
(
n
0
:
3
)
1
)
n
u
(
n
(b) y
(
n
) ¼ (
)
(c) z
(
n
) ¼
u
(
n
) þ d(
n
) þ
0
:
2
)
2
3
n
u
(
n
)
3.3
Evaluate the inverse z-transform of the following function:
z
2
1
6
z
þ
1
1
2
(a) X
(
z
) ¼
,
ROC:
3
<
z
<
5
1
6
z
2
6
z
þ
2z
1
(b) X
(
z
) ¼ log (
1
)
,
ROC: j
z
j >
2
3.4
Determine the z-transform and its ROC for each of the following 2-D sequences:
(a) x
(
n
1
, n
2
) ¼ (
1
n
1
u
(
n
1
)
u
(
n
2
)
2
)
n
1
þ
n
2
u
(
n
1
)
u
(
n
2
)
3.5
Find the eigenvalues and eigenvectors of matrix A given below:
1
(b) y
(
n
1
, n
2
) ¼ (
3
)
12
3
A
¼
1
3.6
Find the eigenvalues and eigenvectors of the following matrices:
2
3
, B
¼
,
013
030
2
1
03
a
b
ba
4
5
A
¼
and
C
¼
300
3.7
Let A be a 4
4 matrix with eigenvalues
1,
2,
3, and
4. Find (if possible)
the following quantities:
(a)
det (
A
T
)
Trace (
A
1
(b)
)
(c)
det (
A
8I
)
3.8
Compute the eigenvalues and eigenvectors of the matrix
2
4
3
5
022
202
220
A
¼
Can matrix A be diagonalized? If yes,
find the transformation to diagonalize
matrix A.
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