Fourier and Laplace
385
fundamental components of the sawtooth
fund. +2nd. harmonic of the sawtooth
0.5
0.5
0.5
−0.5
−0.5
−0.5
0
0
0
Amplitude
Amplitude
Amplitude
Amplitude
fund. +2nd. +3rd. harmonics
0
0
0
1
1
2
2
3
3
4
4
0.5
−0.5
−0.5
−0.5
0.5
0.5
0
0
0
0
1
2
3
4
0
1
2
3
4
0
0.5
1
1.5
2
fund. +2nd. +3rd. +4th. harmonics
fund. +2nd. +3rd. +4th.+ 5th. harmonics
fund. +2nd. +3rd. +4th. +5th. +6th. harmonics
Amplitude
Amplitude
0.5
1
1.5
2
time (in sec)
time (in sec)
FIGURE 4.35
Plots of part c of Example 4.2.
Approximations of the sawtooth wave by sum of harmonics
0.6
0.4
0.2
−0.2
−0.4
−0.6
−0.8
0
Amplitude
0
0.5
1
1.5
2
2.5
3
3.5
4
time (in sec)
FIGURE 4.36
(See color insert following page 374.) Plots of part d of Example 4.2.
CRC_47760_CH004.indd 385
CRC_47760_CH004.indd 385
7/28/2008 12:26:08 PM
7/28/2008 12:26:08 PM