Fourier and Laplace 385
fundamental components of the sawtooth fund. +2nd. harmonic of the sawtooth
0.50.50.5−0.5−0.5−0.5000AmplitudeAmplitudeAmplitudeAmplitudefund. +2nd. +3rd. harmonics000112233440.5−0.5−0.5−0.50.50.500001234012340 0.5 1 1.5 2fund. +2nd. +3rd. +4th. harmonicsfund. +2nd. +3rd. +4th.+ 5th. harmonics fund. +2nd. +3rd. +4th. +5th. +6th. harmonicsAmplitudeAmplitude0.5 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
0.60.40.2−0.2−0.4−0.6−0.80Amplitude0 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.