For the even$-$functioned triangle wave signal defined by

$y(t)=(\frac{8C}{3T})t+C$;$-\frac{T}{2}t0$

$y(t)=-(\frac{8C}{3T})t+C$;$0t\frac{T}{2}$

where C is an amplitude and T is the period:

a$.$ Show that this signal can be represented by the Fourier series

b$.$ Expand the first three nonzero terms of the series. Identify the terms

containing the fundamental frequency and its harmonics.

c$.$ Plot each of the first three terms on a separate graph. Then plot the

sum of the three. For this, set $C=3V$ and $T=2s.$

d$.$ Sketch the amplitude spectrum for the first three terms of this series,

first separately for each term and then combined. Please dont use Al Generated or computer, solve step by step calculations and Sketch the amplitude spectrum for the first three terms of this series, first separately for each term and then combined.