The concept of Fourier series is a powerful means of analyzing periodic waveforms in

Chapter 10, Problem 8

(choose chapter or problem)

The concept of Fourier series is a powerful means of analyzing periodic waveforms in terms of sinusoids. For example, the triangle wave in Fig. 10.45 can be represented by the infinite sum

\(v(t)=\frac{8}{\pi^{2}}\left(\sin \pi t-\frac{1}{3^{2}} \sin 3 \pi t+\frac{1}{5^{2}} \sin 5 \pi t-\frac{1}{7^{2}} \sin 7 \pi t+\cdots\right)\)

where in practice perhaps the first several terms provide an accurate enough approximation. (a) Compute the exact value of v(t) at t = 0.25 s by first obtaining an equation for the corresponding segment of the waveform. (b) Compute the approximate value at t = 0.25 s using the first term of the Fourier series only. (c) Repeat part (b) using the first three terms. (d) Plot v(t) using the first term only. (e) Plot v(t) using the first two terms only. (f) Plot v(t) using the first three terms only.