The Top Part of Figure 8 $F(u)$ For a 1-D Signal $f(i)$

Essay

The top part of Figure 8.1 shows the DCT $F(u)$ for a 1-D signal $f(i)$ .
i. What does $F(5)$ tell you in terms of the image content in $f(i)$ ?
ii. What is the reason that $F(5)$ is less than 0 ?
(b) The Inverse Discrete Cosine Transform (IDCT) can be viewed as a reconstruction process in which the Cosine basis functions are scaled and added one by one to reconstruct $\tilde{f}(i)$ . Assume $F(0)=500$ and $F(1)=-70$ ; in the space provided at the bottom part of the figure,
i. draw $\tilde{f}(i)$ after only the $F(0)$ is used,
ii. draw $\tilde{f}(i)$ after $F(0)$ and $F(1)$ are used.
Show all details including magnitudes, and explain why they look like that.