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Question: Given the difference equation
y[k] + y[k - 1] + (1/4)y[k - 2] = x[k] - x[k - 2]
(i) determine the transfer function representing the LTID system;
(ii) determine the impulse response of the LTID system;
(iii) determine the output of the LTID system to the input x[k] = (1/2)ku[k] using the time-convolution property;
(iv) determine the output of the LTID system by convolving the input x[k] = (1/2)ku[k] with the impulse response obtained in part (ii).
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