Given a system with the transfer function(a) Find the system difference equation.(b) Deter...

Given a system with the transfer function

(a) Find the system difference equation.

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(b) Determine the system modes.

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(c) From Part (b), determine the system’s natural response. (Do not solve for the unknown constants.)

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(d) Find the system’s steady-state response when x[n] = cos(0.2n).

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(e) Use MATLAB to verify the results of Part (d).

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(f) Show that the response found in Part (d) satisfies the system difference equation.

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(g) Find the system’s steady-state response when x[n] = cos[(0.2π + 0.2)n].

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(h) Use MATLAB to verify the results of Part (g).

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(i) Comment on any significant aspects of the results in Parts (d) and (g).