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)’) ;
CRC_47760_CH001.indd 31
CRC_47760_CH001.indd 31
7/25/2008 4:16:16 PM
7/25/2008 4:16:16 PM