PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 393

line spectrum

frequency w (in rad/sec)

0.6

0.4

0.2

0.25

0.2

0.15

0.1

0.05

−0.2

Amplitude of Fn^0

− 20 − 15 − 10 − 5 0 5 10 15 20

power spectrum

0

Magnitude of Fn

2

− 20 − 15 − 10 − 5 0 5 10 15 20

frequency w (in rad/sec)

FIGURE 4.43

Plots of parts d and e of Example 4.4.

Note that the function f(t) in this example is similar to the function analyzed in

Exa mple 4.1. The differences are a DC shift in magnitude by 1 and a time shift

by 0.5 s.

Observe that simple shifts change the symmetry conditions of the function f(t), creat-

ing new harmonics.

Example 4.5

Create the script fi le Fourier_coeff that returns the fi rst fi ve coeffi cients of the exponential

FS (F 1 , F 2 , F 3 , F 4 , and F 5 ), of the function of Example 4.1, given by

ft

n

nw t

n

()
 ( )

217

^0

odd

∑ sin

by using

1. Symbolic techniques


2. Numerical techniques


3. Compare the results of part 1 with part 2

MATLAB Solution

% Script file : Fourier _ coeff

T = 2;w0 = 2*pi/T; nn =1:5;