A periodic signal x(t) with a period T0 = 10 is described over one period, 0 ≤ t ≤ 10, by...

A periodic signal x(t) with a period T0 = 10 is described over one period, 0 ≤ t ≤ 10, by the equation

This signal can be represented by the Fourier series (3.19) which is valid for all time —∞

(a) Sketch the periodic function x(t) over the time interval −10 ≤ t ≤ 20.

(b) Determine the DC coefficient of the Fourier series, a0.

(c) Use the Fourier analysis integral (3.21) to find a1, the first Fourier series coefficient (i.e., for k = 1).

(d) If we add a constant value of one to x(t), we obtain the signal y(t) = 1 + x(t) with y(t) given over one period by

This signal can also be represented by a Fourier series, but with different coefficients:

Explain how b0 and b1 are related to a0 and a1. Note: You should not have to evaluate any new integrals explicitly to answer this question.