PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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)]