Signals and Systems - Electrical Engineering

1.4 Representation Using Basic Signals 97

− 10 − (^50510)
− 1
−0.5
0
0.5
1
1.5
2
t
x(
t)
− 2 − 1 0 1 2 3 4
− 8
− 6
− 4
− 2
0
2
4
6
8
t
(a) (b)
y(
t)
1 +3/2 cos(1/5πt)−3/5 cos(2/5πt)
FIGURE 1.10
(a) Damped sinusoid, and (b) sum of weigthed cosines approximating a pulse.
hold on
ezplot(-y,[-2,4])
axis([-2 4 -8 8])
hold off
The approximate pulse signal is generated by the following script.
clear; clf
t = sym(’t’);
% sum of constant and cosines
x = 1 + 1.5 cos(2 pi t/10)-.6 cos(4 pi t/10);
ezplot(x,[-10,10]); grid
The plots of the damped sinusoid and the approximate pulse are given in Figure 1.10. n
nExample 1.19
Consider the generation of a triangular signal,
3(t)=







t 0 ≤t≤ 1

−t+2 1<t≤ 2

0 otherwise

using ramp signalsr(t). Use the unit-step signal to represent the derivative ofd3(t)/dt.

Solution

The triangular pulse can be represented as

3(t)=r(t)− 2 r(t− 1 )+r(t− 2 ) (1.32)