We want to use the Fourier series of a train of square pulses (done in the chapter) to compute the Fourier series of the triangular signal x(t)with a period

x₁(t) = r(t) − 2r(t − 1) + r(t − 2)

(a) Find the derivative of x(t)or y(t) = dx(t)/dt and carefully plot it. Plot also z(t) = y(t) + 1. Use the Fourier series of the train of square pulses to compute the Fourier series coefficients of y(t) and z(t).

(b) Obtain the sinusoidal forms of y(t) and z(t) and explain why they are represented by sines and why z(t) has a non-zero mean.

(c) Obtain the Fourier series coefficients of x(t) from those of y(t).

(d) Obtain the sinusoidal form of x(t) and explain why the cosine representation is more appropriate for this signal than a sine representation.