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
- Symbolic techniques
- Numerical techniques
- Compare the results of part 1 with part 2
MATLAB Solution
% Script file : Fourier _ coeff
T = 2;w0 = 2*pi/T; nn =1:5;