Digital Signal Processing Reference
In-Depth Information
10.31.
You are given a system that is known to be time-invariant.
When input to the system, a discrete time signal
x
1
[n]
produces an output
y
1
[n]
where
x
1
[n] = d[n] + d[n - 1] + d[n - 2]
and
y
1
[n] = 2d[n + 1] + 2d[n] + 2d[n - 1].
A second discrete time signal
x
2
[n]
produces an output
y
2
[n]
where
x
2
[n] = d[n - 1] - d[n - 2]
and
y
2
[n] = 2d[n] - 2d[n - 1].
A third discrete time signal
x
3
[n]
produces an output
y
3
[n]
where
x
3
[n] = d[n] + d[n - 1] + 2d[n - 2] - d[n - 3]
and
y
3
[n] = 2d[n + 1] + 2d[n] + 3d[n - 1] - 2d[n - 2].
Determine whether or not the system is linear. Justify your answer.
10.32.
You are given a system that is known to be time-invariant. When input to the system,
a discrete time signal
x
1
[n] = 2d[n - 3]
produces an output
y
1
[n] = 2d[n - 2] + 4d[n - 3].
A second discrete time signal
x
2
[n] = 2d[n - 1] + 2d[n - 3]
produces an output
y
2
[n] = 2d[n - 2] + 6d[n - 3] + 4d[n - 4].
Determine whether or not the system is linear. Justify your answer.
