PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 31

area _ step =

3

>> area _ sign = int(‘signum(t)’, -2, 3) % area of the sign from

–2 to +3

area _ sign =

1

>> stept _ 3 = vpa(‘Heaviside(3)’) % evaluates u(t) at t =3

stept _ 3 =

1

>> stepmin _ 2 = vpa(‘Heaviside(-2)’) % returns u(t) at t = -2

stepmin _ 2 =

0

>> differstep = diff(‘Heaviside(t)’) % returns d(u(t))/dt

differstep =

Dirac(t)

>> intramp = int(‘Heaviside(t)’*t) % returns the integral

of t u(t) dt

intramp =

1/2*Heaviside(t)*t^2

>> area _ ramp12 = int(‘Heaviside(t)’*t,1,2) % area of [t u(t)] from

t =1 to t =2

area _ ramp12 =

3/2

>> area _ ut _ 12 = int(‘Heaviside(t)’*t,-1,2) % area t u(t) from t = –1

to t =2

area _ ut _ 12 =

2

>> area _ signt = int(‘signum(t)’*t,-1,2) % area sign(t)*t from t=–1

to t=2

area _ sign =

5/2

R.1.104 Create the script fi le plot_ramp that returns the plot of t u(t) versus t, over the range

− 1 ≤ t ≤ 3 , using ezplot.

MATLAB Solution

% Script file: plot _ ramp

ramp = (‘Heaviside(t)’*t) % returns the ramp over

–1 ≤ t ≤3

ezplot(ramp, [-1 +3]) % see plot Figure 1.29

title(‘heaviside(t)*t vs. t’);

xlabel(‘t’); ylabel(‘t*u(t)’) ;