A signal x(t) is periodic with period T0 = 8. Therefore, it can be represented as a Fourie...

A signal x(t) is periodic with period T0 = 8. Therefore, it can be represented as a Fourier series of the form

It is known that the Fourier series coefficients for this representation of a particular signal x(t) are given by the integral

(a) In the integral expression for ak above, the integrand and the limits define the signal x(t). Determine an equation for x(t) that is valid over one period.

(b)Using the result from part (a), draw a plot of x(t) over the range – 8 ≤ t ≤ 8 seconds. Label your plot carefully.

(c) Determine the DC value of x(t).