Suppose you have two programs for computing the DFT of a sequence x n that has N 2 v nonzero samples Program A computes the DFT by directly implementing the definition of the DFT sum from Eq and takes N 2 seconds to run Program B implements the decimation in time FFT algorithm and takes 10N log 2 N seconds to run What is the shortest sequence N such that program B turns faster than program A N 1 Analysis equation X k n w (8 67) 3D

Question: Suppose you have two programs for computing the DFT of a sequence x[n] that has N = 2 v nonzero samples. Program A computes the

Suppose you have two programs for computing the DFT of a sequence x[n] that has N = 2^v nonzero samples. Program A computes the DFT by directly implementing the definition of the DFT sum from Eq. 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 turns faster than program A?

N-1 Analysis equation: X[k] = *[n]w". (8.67) %3D

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