Text: Express each of the waveforms below in terms of step functions and then determine its Laplace transform. (Recall that the ramp function is related to the step function by r(t - T) = (t - T)(t - T).) Assume that all waveforms are zero for t < 0.
x1
x2 2J
Staircase
Square wave
2
0
t (s)
1
2
3
0
t (s)
2+
-
2
(a)
(b)
x3
X4
Top hat
Mesa
4
2
t (s)
0
ts
-
3
4
2
6
7
(c)
(d)
x6
x5
Negative ramp N
10
Triangular wave
0
ts
0
ts
2
6
10
-01
(c)
(f)
(a) Staircase
(b) Square wave
(c) Top hat
(d) Mesa
(e) Negative ramp
(f) Triangular wave