Using a dft magnitude spectrum estimate the spectral

Question

Question: Consider the following deterministic signal:

x₁[k] = 2 sin(0.2πk) + 3 cos(0.5πk).

Using a DFT magnitude spectrum, estimate the spectral content of x[k] for the following cases:

(a) a 20-point DFT and a sample size of 0 ≤ k ≤ 19;

(b) a 32-point DFT and a sample size of 0 ≤ k ≤ 31;

(c) a 64-point DFT and a sample size of 0 ≤ k ≤ 31;

(d) a 128-point DFT and a sample size of 0 ≤ k ≤ 31; and

(e) a 128-point DFT and a sample size of 0 ≤ k ≤ 63. Comment on the leakage effect in each case.