Question: Computation of the DFT use an FFT subroutine to compute the following DFTs and plot the magnitudes |X(k)| of the DFTs. (a) The 64-point DFT

Computation of the DFT use an FFT subroutine to compute the following DFTs and plot the magnitudes |X(k)| of the DFTs.

(a) The 64-point DFT of the sequence

(b) The 64-point DFT of the sequence

(d) The 64-point DFT of the sequence

Answer the following questions.

(1) What is the frequency interval between successive samples for the plots in parts (a), (b), (c), and (d)?

(2) What is the value of the spectrum at zero frequency (dc value) obtained from the plots in parts in parts (a), (b), (c), (d)?

From the formula, compute the theoretical values for the dc value and check these with the computer results.

(3) In plots (a), (b), and (c), what is the frequency interval between successive nulls in the spectrum? What is the relationship between N₁ of the sequence x(n) and the frequency interval between successive nulls?

(4) Explain the difference between the plots obtained from parts (a) and (c).

(a) n= v, 1,.... 15 0, 16) 1, x(n) = l (N,

(a) n= v, 1,.... 15 0, 16) 1, x(n) = l (N, otherwise (b) n = 0. 1...., 7 1. 1(n) = (N = 8) otherwise (d) n= 0, 1... ..63 (N = 64) 10en x(n) = 0. otherwise (2) N-1 X (k) = > 'x(n)e-(27/N ink

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