Problem $2(15$ points$)$

Consider the following signal

$x(t)=e^{j2t}+e^{j4t}$

$(1)$ Determine the fundamental period $T$ of $x(t).$

$(2)$ Determine the Fourier series of $x(t)$ under the period $T.$

$(3)$ Determine the Fourier transform of $x(t).$

$54t$

$(4+j2),(4-j2)$