PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 15

the system differential equation.* Note also that when b is complex, then by Euler’s

equalities f(t) presents oscillations.

Finally, the more common equation f(t) = Ae−bt u(t) is defi ned analytically by

ft

Ae t

t

bt

()

 



for

for

0

00







R.1.36 An exponential sequence can be defi ned by f(n) = A an, for −∞ ≤ n ≤ ∞, where a can

be a real or complex number.

R.1.37 The following example illustrates the form of an exponential function for various

values for A and b.

Let us explore the behavior of the exponential function, by creating the script fi le

exponentials that returns the following plots:

a. f 1 (t) = 4e(−t/2)

b. f 2 (t) = 4e(t/ 2)

c. f 3 (t) = 4e(−t/2)u(t)

d. f 4 (t) = −4e(t/ 2)u(t)

for A = ± 4 and b = ±1/2, over the range − 3 ≤ t ≤ 3 , using 61 elements.

MATLAB Solution

% Script file: exponentials

t = -3:.1:3;

ft1 = 4*exp(-t./2);

ft2 = 4*exp(t./2);

ut _ 1 = [zeros(1,30) ones(1,31)]; % step with 61 elements

ft3 = ft1.*ut _ 1;

subplot(2,2,1);

plot(t, ft1);

axis([-3 3 -.5 18]);xlabel(‘t (time)’)

title(‘f1(t)=4*exp(-t/2) vs. t’);

ylabel(‘Amplitude [f1(t)]’)

subplot(2,2,2);

plot(t, ft2); xlabel(‘t (time)’)

axis([-3 3 0 20]);

title(‘f2(t) = 4*exp(t/2) vs. t’);

ylabel(‘Amplitude [f2(t)]’);

subplot(2,2,3);

plot(t, ft3);

axis([-3 3 -.5 5]);

title(‘f3(t) =4*exp(-t/2)*u(t) vs. t’);

xlabel(‘t (time)’)

ylabel(‘Amplitude[f3(t)]’);

subplot(2,2,4);

ft4 =-1.*ft2.*ut _ 1;

plot(t, ft4);

axis([-3 3 -20 1]);

title(‘f4(t) = -4*exp(-t/2)*u(t) vs. t’)

xlabel(‘t (time)’); ylabel(‘Amplitude[f4(t)]’);

The script fi le exponentials is executed and the results are shown in Figure 1.17.

*^ See Chapter 7, Practical MATLAB® Basics for Engineers.