Consider the linear time invariant system
with the impulse response

_{} .

Determine the output *y*(**t) **when the input is

_{} .

The input and the impulse response of a linear,
time-invariant system are shown in Fig. (a) and Fig. (b) respectively.

**a)
**Determine the output y(t).

**b) **Determine
if this system is stable. Explain.

**a) **

Find the impulse response of the causal and LTI system S1 described by:

_{}.

Is this system stable? Explain.

**b) **The
system in part (a) is cascaded to a system S2 with input-output relationship _{}, as shown in figure (a). Find the response of the cascaded
system when the input is a unit impulse.

**c) **Repeat
part (b) with order of cascade connection is changed as shown
in figure (b) and compare the results. Is the output changed? Why?

A linear, time-invariant causal system is characterized by
the transfer function _{} .

Determine and sketch the impulse respone
of this system.

The
response *y*(t)
of the continuous-time LTI system for the input _{} is given to be _{}.

a)
Determine the transfer function *H*(s) of the system.

b)
Determine the impulse response *h*(t) of the system.

Determine the

A linear, time-invariant system is
characterized by the differential equation

_{}.

**a) **Determine
the impulse response of this system.

**b) **Determine
the output *y(*** t)** when the input is

**c) **Is
this system stable? Explain.

Determine the
impulse response of the LTI system described by the differential equation:

**a) **_{}

**b)
**_{}

**c) **_{}.

A signal x(t),
which is zero for t negative, has the _{}. Determine:

**i)
**_{}

**ii) **_{}

**iii) **_{}

Consider the signal x(t) shown in the figure.
Determine the _{*}x(t-1), using
the properties of

A linear, time-invariant
causal system is characterized by the differential equation

_{}.

**a) **Determine
the impulse response of this system.

**d) **Is
this system stable? Explain.

**e) **Making
use of the above, determine the impulse response of the LTI system described by
the differential equation

_{}.