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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 (ejω) of x(n) and plot the magnitude and phase of X(ejω). You need to properly define the resolution of X(ejω) in the frequency domain.
(c) Verify that the above DFT is the sampled version of X(ejω). 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(ejω) 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.
Output Statements: disp and fprintf: The Output statements display strings and the answers of expressions and can permit for formatting or customizing how they are exhibited.
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Various commands for get the help: There are various commands which can serve as an introduction to MATLAB and allow you to get the help: info will show contact informatio
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