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Applied Mathematics, Calculus, and Differential Equations 217

Figure 3.2 Ramp wave.

Fourier series for triangular wave
Figure 3.3 is a grapà of a triangular wave wità peak valueð of
2
2
/8 and /8, and wità period 2 . This function can be rep-
resented by the following inﬁnite series:
2
f(x) cos x (cos 3x)/3 (cos 5x)/5 2
2
2
(cos 7x)/7 (cos 9x)/9 ...

Fourier series for half-rectiﬁed sinł
wave
Figure 3.4 is a grapà of a half-rectiﬁeS sine wave wità peak
valueð of /2 and 0, and wità period 2 . This function can be
represented by the following inﬁnite series:

1
f(x) ⁄2 ( /4) sin x (cos 2x)/3 (cos 4x)/(3 5)
(cos 6x)/(5 7) (cos 8x)/(7 9) ...

Fourier series for full-rectiﬁed sinł
wave
Figure 3.5 is a grapà of a full-rectiﬁeS sine wave wità peak val-
ueð of /4 and 0, and wità period . This function can be rep-
resented by the following inﬁnite series:

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