According to the DCT$-N$ definition above, $F_N(1)$ and $F_N(N-1)$ are the $AC$

coefficients representing the lowest and highest spatial frequencies, respectively.

$($a$)$ It is known that $F_{16}(1)$ and $F_8(1)$ do not capture the same $($lowest$)$ frequency

response in image filtering. Explain why.

$($b$)$ Do $F_{16}(15)$ and $F_8(7)$ capture the same $($highest$)$ frequency response?