364
Practical MATLAB
® Applications for Engineers
R.4.115 The following examples illustrate the procedure used to obtain the LT of the standard time functions (signals or systems) using the symbolic MATLAB toolbox.
Obtain the LT of the following time-dependent functions, and compare the
results with the transforms of Table 4.2.
a. f1(t) = exp(t)
b. f2(t) = t exp(t)
c. f3(t) = cos(t)
d. f4(t) = sin(t)
e. f5(t) = t
7
f. f6(t) = u(t)
g. f7(t) = pul(t/2)
MATLAB Solution
>> syms s t x ;
>> F1 = laplace(exp(t))
% part (a)
F1 =
1/(s-1)
>> F2 = laplace(t*exp(t))
% part (b)
F2 =
1/(s-1)^2
>> F3 = laplace(cos(t))
% part (c)
F3 =
s/(s^2+1)
>> F4 = laplace(sin(t))
% part (d)
F4 =
1/(s^2+1)
>> F5 = laplace(t^7)
% part (e)
F5 =
5040/s^8
>> F6 = laplace(sym(‘Heaviside(t)’))
% part (f)
F6 =
1/s
>> F7 = laplace(sym(‘Heaviside(t+1)’)
-sym(‘Heaviside(t-1)’))
% part(g)
F7 =
1/s-exp(-s)/s
Note that the transforms obtained using the symbolic MATLAB toolbox fully
agree with the transforms of Table 4.2.
R.4.116 The MATLAB function f = ilaplace(F), where F is a symbolic expression with independent variable s, returns the ILT of F, denoted by f which is a function of t,
denoted by F(s) → f(t).
CRC_47760_CH004.indd 364
CRC_47760_CH004.indd 364
7/28/2008 12:26:03 PM
7/28/2008 12:26:03 PM