Read each part of this problem carefully to note the differences among parts. (a) Consi...

Read each part of this problem carefully to note the differences among parts.

(a) Consider the signal

which can be represented by the IDFT equation as

where X₈[k] is the eight-point DFT of x[n]. Plot X₈[k] for 0 ≤ k ≤ 7.

(b) Determine V₁₆[k], the 16-point DFT of the 16-point sequence

Plot V₁₆[k] for 0 ≤ k ≤ 15.

(c) Finally, consider |X₁₆[k]|, the magnitude of the 16-point DFT of the eight-point sequence

Plot |X₁₆[k]| for 0 ≤ k ≤ 15 without explicitly evaluating the DFT expression. You will not be able to find all values of |X₁₆[k]| by inspection as in parts (a) and (b), but you should be able to find some of the values exactly. Plot all the values you know exactly with a solid circle, and plot estimates of the other values with an open circle.