Time Domain Representation of Continuous and Discrete Signals
59
MATLAB Solution
% Script file: analog _ func
t = -1:0.01:5;
t0 = 0;
ut = stepfun(t,t0);
% u(t)
t0 =1;
ut1 =stepfun(t,t0);
% u(t-1)
t0 = 2;
ut2 = stepfun(t,t0);
% u(t-2)
t0 = 3;
ut3 = -3 * stepfun(t,t0);
% -3u(t-3)
fn = ut+ut1+ut2+ut3;
plot(t,fn);
axis([-1 5 -1 4])
title(‘f(t) = u(t) + u(t-1) + u(t-2) - 3u(t-3) ‘)
xlabel(‘time t’)
ylabel(‘Amplitude [f(t)]’)
The script fi le analog-func is executed and the result is shown in Figure 1.50.
Example 1.3
Create the script fi le sequences that uses MATLAB to verify graphically that the discrete
sequences f 1 (n) and f 2 (n), defi ned as follows, over the range −10 ≤ n ≤ 10 are equal:
ƒ 1 (n) = 3 u(−n) * u(n + 5)
and
ƒ 2 (n) = 3[u(n + 5) − u(n + 1)]
MATLAB Solution
% Script file: sequences
clc; clf;
yzero = [zeros(1,21)]; n=-10:10;
n0 = 0;un = stepfun(n, n0);
FIGURE 1.50
Plot of Example 1.2.
−1
0
1
2
3
4
5
−1
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
f(t) = u(t) + u(t − 1) + u(t − 2) − 3u(t − 3)
time (t)
Amplitude [f(t)]
CRC_47760_CH001.indd 59
CRC_47760_CH001.indd 59
7/25/2008 4:16:22 PM
7/25/2008 4:16:22 PM