PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 29

The step function called Heaviside is indicated as follows:

function stepseq = Heaviside(x)

stepseq = (x>=0);

R.1.98 For example, write a program that returns u(t) and u(t − 2), using the function

Heaviside, over the range − 10 ≤ t ≤ 10.

MATLAB Solution

>> x = -10:0.1:10;

>> stepfun = Heaviside(x);

>> subplot(2, 1, 1);

>> plot(x, stepfun)

>> xlabel(‘t (time)’)

>> title(‘u(t) vs. t’)

>> ylabel(‘Amplitude.’)

>> axis([-10 10 ,0.5 1.5])

>> subplot(2, 1, 2);

>> stepfun = Heaviside(x-2);

>> plot(x, stepfun)

>> axis([-10 10 ,0.5 1.5])

>> title(‘u(t-2) vs. t’)

>> ylabel(‘Amplitude.’);

>> xlabel(‘t (time)’);

See Figure 1.27.

R.1.99 The MATLAB function sign(t) is defi ned as follows:

sign t

t

t

t

()





10

00

 10











The sign(t) function is illustrated in Figure 1.28.

FIGURE 1.27

Plots of u(t) and u(t − 2) of R.1.98.

1.5

Amplitude

Amplitude

1

− 10 − 8 − 6 − 4 − 2 0246810

0.5

1.5

1

0.5

− 10 −^8 −^6 − 4 − 2 024 6 8 10

t (time)

u(t) versus t

u(t−2) versus t

t (time)