Page 253 - Numerical Analysis Using MATLAB and Excel

Chapter 6 Fourier, Taylor, and Maclaurin Series

1.2
K=5
1
0.8

0.6
0.4
0.2
0

-0.2
-0.4
-4 -3 -2 -1 0 1 2 3 4

Figure 6.27. Line spectrum of (6.109) for k = 5

1.2
K=10
1
0.8

0.6
0.4
0.2

0
-0.2

-0.4
-4 -3 -2 -1 0 1 2 3 4

Figure 6.28. Line spectrum of (6.112) for k = 10

The spectral lines are separated by the distance 1k⁄ and thus, as gets larger, the lines get closer
k
together while the lines are further apart as gets smaller.
k

6.8 Numerical Evaluation of Fourier Coefficients

Quite often, it is necessary to construct the Fourier expansion of a function based on observed
values instead of an analytic expression. Examples are meteorological or economic quantities

6−36 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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