2. [20 points] Consider the signal g(t) = t over the interval (-,) and it's periodic extension.

(a) Find the exponential Fourier series (F.S.) for g(t).

(b) From the exponential F.S., plot the amplitude and phase spectrum.

(c) Find the compact trigonometric Fourier series for g(t).

(d) Plot the approximated signal you obtain via the Fourier Series with (i) the DC component only; (ii)

up to the first harmonic, and (iii) up to the second harmonic.

(e) Using Parseval's theorem (for exponential Fourier Series of this g(t)), prove that

3-43

n=1