Solve the following problem:
Let x(n) be a finite-duration signal with length N and let X(k) be its N-point DFT. Suppose we pad x(n) with L zeros and compute the (N + L)-point DFT, X'(k). What is the relationship between X(0) and X'(0)? If we plot |X(k)| and |X'(k)| on the same graph, explain the relationships between the two graphs.