User`s guide
102
The three components are combined to form the Fourier series:
The limit of the Fourier series approaches the exact value of the periodic function as the
number of terms in the series approaches infinity. The Fourier series become an approximation
when the series includes a finite number of terms. More terms in the series expansion, closer the
approximation of the original function, as demonstrated in Figure 4 Fourier serious expansion of a
periodic sawtooth wave (L=1). The number of terms in the series varies from one, two, to five and 25.
, which contains Fourier series approximations of a saw tooth signal with 1 term, 2 terms,
5 terms and 25 terms.
Figure 4 Fourier serious expansion of a periodic sawtooth wave (L=1). The
number of terms in the series varies from one, two, to five and 25.
The derivation of the Fourier functions for a periodic sawtooth wave is shown below.
Consider a string of length 2L plucked at the right end and fixed at the left. The
functional form of this configuration is
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8
N=1
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8
N=2
-0.5
0
0.5
1
1.5
0 2 4 6 8
N=5
-0.5
0
0.5
1
1.5
0 2 4 6 8
N=25
Eq.42
Eq.44
Eq.43