Suppose you have a signal x[n] with 1021 nonzero samples whose discrete-time Fourier transform you wish to estimate by computing the DFT. You find that it takes your computer 100 seconds to compute the 1021-point DFT of x[n]. You then add three zero-valued samples at the end of the sequence to form a 1024-point sequence x₁[n]. The same program on your computer requires only 1 second computing X₁[k]. Reflecting, you realize that by using x₁[n], you are able to compute more samples of X(e ^jω) in a much shorter time by adding some zeros to the end of x [n] and pretending that the sequence is longer. How do you explain this apparent paradox?