We want to use the Fourier series of a train of square pulses (done in the chapter)
Question:
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.
Step by Step Answer:
a The derivative of the period between 0 and 2 of the triangular signal xt is and the signal is a tr...View the full answer
