Suppose you have two programs for computing the DFT of a sequence x[n] that hasN = 2ν nonzero samples. Program A computes the DFT by directly implementing the definition of the DFT sum from Eq. (8.67) and takes N2 seconds to run. Program B implements the decimation-in-time FFT algorithm and takes 10N log2 N seconds to run. What is the shortest sequence N such that Program B runs faster than Program A?
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