a$)$ Are${}_1(t)=1,{}_2(t)=$exp$(jt)$ and ${}_3(t)=$exp$(-jt)$ are the or thogonal basis signals over the interval $[02]?$ Justify your answer. $(12$ points$)$

b$)$ Express $x(t)=cost$ in teris of ${}_1(t),{}_2(t)$ and ${}_3(t)$ by calculating the coefficients. $(6$ po

c$)$ Find the exponential Fourier series and the trigonometric Fourier series of $x(t)=cost.(18$ p

d$)$ Find the Fourier transform of $x(t)$ using the Fourier series of $x(t).(2$ points$)$

e$)$ Find the Fourier transform of $x(t)$ using the linear property. $(2$ points$)$