Question: The following are three different signals x i [n] that are the sum of two sinusoids: x 1 [n] = cos (n/4) + cos (17n/64),

The following are three different signals x_i[n] that are the sum of two sinusoids:

x₁[n] = cos (πn/4) + cos (17πn/64),

x₂[n] = cos (πn/4) + 0.8 cos (21πn/64),

x₃[n] = cos (πn/4) + 0.001 cos (21πn/64).

We wish to estimate the spectrum of each of these signals using a 64-point DFT with a 64-point rectangular window w[n]. Indicate which of the signals’ 64-point DFTs you would expect to have two distinct spectral peaks after windowing.

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