38 sketch the continuous time signals f t g t find

2.3.8 Sketch the continuous-time signals f ( t ), g ( t ).
Find and sketch the convolution y ( t ) = f ( t ) ⇤ g ( t ).
f ( t ) = e
- t
u ( t ) ,
g ( t ) = e
- t
u ( t )
2.3.8) Solution
253

2.3.11 Sketch the continuous-time signals f ( t ), g ( t ).
Find and sketch the convolution y ( t ) = f ( t ) ⇤ g ( t ).
f ( t ) = u ( t + 2) - u ( t - 2)
g ( t ) =
1 X
k = -1
δ ( t - 3 k )
2.3.11) Solution
256

2.3.12 Sketch the convolution of the following two signals.
1
0 1 2 3 4 5
t
f ( t )
1
0 1 2 3 4 5
t
g ( t )
2.3.12) Solution
257

2.3.13 Consider the cascade connection of two continuous-time LTI systems
x ( t )
-
SYS 1
-
SYS 2
-
y ( t )
with the following impulse responses,
h
1
( t )
-
- 1
0 1 2 3
1
h
2
( t )
-
- 1 0 3
1
- 1
Accurately sketch the impulse response of the total system.
259

2.3.13) Solution
260

2.3.14 Two continuous-time LTI systems are connected in cascade.
x ( t ) h
1
( t ) h
2
( t ) y ( t )
The impulse responses of the two systems are:
1
-1
0 3 4 5
t
h
1
( t )
1
-1
0 1 3 5
t
h
2
( t )
Sketch the impulse response of the total system.
2.3.14) Solution
OVERLAPPING
261