Digital Signal Processing Reference
In-Depth Information
x
(
t
)
y
(
t
)
1/
a
n
b
n
a
n
1
b
n
1
a
n
2
b
n
2
a
1
b
1
a
0
b
0
Figure 3.29
Direct form II for an
n
th-order system.
realizing analog filters and in developing analog and digital simulations of a system.
However, in simulating a system, we prefer an internal model such that the outputs
of the integrators represent physical variables, as much as possible.
In this chapter, we consider continuous-time linear time-invariant (LTI) systems.
First, it is shown that a continuous-time signal can be expressed as a function of an
impulse function. This representation is in the form of an integral and allows us to
describe the input-output characteristics of an LTI system in terms of its impulse
response.
Describing a system by its impulse response is basic to the analysis and design
of LTI systems; the impulse response gives a complete input-output description of
an LTI system. It is shown that the input
x(t),
the impulse response
h(t),
and the
output
y(t)
are related by the convolution integral:
q
q
y(t) =
L
x(t)h(t - t)dt =
L
x(t - t)h(t)dt.
-
q
-
q
