Suppose you have a signal x[n] with 1021 nonzero samples whose DTFT 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 to compute X1[k]. Reflecting, you realize that by using x1[n], you are able to compute more samples of X(ejω) 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?
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