If $x(t)$ and $y(t)$ are both continuous time periodic signals with period $T_0$ and Fourier representation given by: and

Show that the Fourier series coefficients of the signal are given by discrete convolution

Fourier Transforms

P$1$: Determine the Fourier transform of the following signals

a$)x(t)=e^{-at}u(t)$;$a>0$

b$)x(t)=e^{-\text{a}\text{l}\text{t}},$;$a>0$

c$)x(t)=$Sin$(t)$

d$)x(t)=(t)$