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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.
A filter described by the equation: y(n) = x(n) + x(n-1) + 0.9 y(n-1) - 0.81 y(n-2) (a) Find the transfer function H(z) for the filter and find the poles and zeros of the fil
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use the loop for to produce [-1 -1 -1 -1; 0 -1 -1 -1; 0 0 -1 -1; 0 0 0 -1]
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Calculating and Visualizing Sequence Statistics Follow the instructions in this demo file to download a sequence and calculate and visualize its statistics. Save all the command
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Ft. Loudoun and Watts Bar are two large hydroelectric dams, the former upstream of the latter. The level of Watts Bar Lake must be kept within limits for recreational purposes, and
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