a 12-point sequence is x n defined as xn 1 2 3

Question

A 12-point sequence is x (n) defined as x(n) = { 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1}. Write MATLAB programs to

(a) Determine the DFT X (k) of x(n) and plot (using stem function) its magnitude and phase.

(b) Determine the DTFT X (e^jω) of x(n) and plot the magnitude and phase of X(e^jω). You need to properly define the resolution of X(e^jω) in the frequency domain.

(c)  Verify that the above DFT is the sampled version of X(e^jω). It might be helpful to combine the above two plots in one graph using the hold function.

(d)  Is it possible to reconstruct the DTFT X(e^jω) from the DFT of X(k)? If possible, give the necessary interpolation formula for reconstruction. If not possible, state why this construction cannot be done.

The programs generating the plots should be provided.