Digital Signal Processing Reference
In-Depth Information
(a)
Is this system linear?
(b)
Is this system time invariant?
(c)
Determine the response to the input
(d)
Determine the response to the input
d(t).
d(t - p/2).
From examining this result, it is
evident that this system is not time invariant.
3.21.
Determine the stability and the causality for the LTI systems with the following im-
pulse responses:
h(t) = e
-t
u(t - 1)
(a)
(b)
(c)
(d)
(e)
(f)
h(t) = e
(t - 1)
u(t - 1)
h(t) = e
t
u(1 - t)
h(t) = e
(1 - t)
u(1 - t)
h(t) = e
t
sin(-5t)u(-t)
h(t) = e
- t
sin(5t)u(t)
3.22.
Consider an LTI system with the input and output related by
q
e
-t
x(t - t)dt.
y(t) =
L
0
(a)
Find the system impulse response
h(t)
by letting
x(t) = d(t).
(b)
Is this system causal? Why?
(c)
Determine the system response for the input shown in Figure P3.22(a).
(d)
Consider the interconnections of the LTI systems given in Figure P3.22(b), where
is the function found in Part (a). Find the impulse response of the total system.
(e)
Solve for the response of the system of Part (d) to the input of Part (c) by doing the
following:
(i)
y(t)
h(t)
Use the results of Part (c). This output can be written by inspection.
(ii)
Use the results of Part (d) and the convolution integral.
x
(
t
)
1
1
0
t
(a)
h
(
t
)
(
t
1)
h
(
t
)
(b)
Figure P3.22
