For a signal points total$)$

a$.$ Show the steps to find the smallest sampling time needed to avoid leakage. $(4$ points$)$

$T_1=\frac{\frac{1}{\frac{1}{2}}}{?}=2$

$T_2=\frac{1}{\frac{1}{3}}=3,T_5=n{T}_1=m{T}_2$

$\frac{n}{m}=\frac{T_2}{T_1}$

$n,n$

$,$

$T_5,=23$

$,=6sec$

b$.$ Show the steps to find the frequency resolution if an FFT is performed to the sampled signal. $(3$ points$)$

$\frac{1}{T_5}=\frac{1}{65}$