Signals and Systems - Electrical Engineering

2.3 LTI Continuous-Time Systems 137

FIGURE 2.8
Response of an RL
circuit to a pulse
v(t)=u(t)−u(t− 2 )
using superposition and
time invariance.

i(t

),

−

i(t

−

2)

i(t

)−

i(t

−

2)

− 1 0 1 4 5 67

− 2

− 1

0

1

23

2

i(t)

−i(t−2)

− 1 0 1 2 3 4 5 67

0

0.5

1

1.5

2

t (sec)

FIGURE 2.9
Application of
superposition and
time invariance to
find the response of
an LTI system.

01 01

(^12123)
2
1
1
0
− 1
0.5
0.5
−0.5
0
t t
t t
v 1 (t) i 1 (t)
−i 1 (t−1)
v(t) i(t)
i 1 (t)
Recall that the generic representation of a signalx(t)in terms of shiftedδ(t)signals found in Chapter 1
is given by
x(t)=

∫∞

−∞

x(τ)δ(t−τ)dτ (2.17)