For the causal discrete-time LTI system implemented using the difference equation y/n] = -0.25y[n 1]...

 

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For the causal discrete-time LTI system implemented using the difference equation y/n] = -0.25y[n – 1] + 0.125y[n – 2] + 4x[n] + 0.25x[n – 1] where a[n] is the input signal, and y(n] is the output signal. Draw the direct form-II block diagram of the system. а. b. Find the transfer function of the system, H(2). Sketch the pole-zero diagram and indicate the ROC. Determine if the Fourier transform of the system H(eiw) exists. If the Fourier transform exists, write H(eju). с. d. Find the z-transform of the output, Y(2), when the input is x[n] = u[-n – 1]. Specify the ROC for Y(2). Z-Transform Definition : X(z) A ) «[n]z" n=-00 For the causal discrete-time LTI system implemented using the difference equation y/n] = -0.25y[n – 1] + 0.125y[n – 2] + 4x[n] + 0.25x[n – 1] where a[n] is the input signal, and y(n] is the output signal. Draw the direct form-II block diagram of the system. а. b. Find the transfer function of the system, H(2). Sketch the pole-zero diagram and indicate the ROC. Determine if the Fourier transform of the system H(eiw) exists. If the Fourier transform exists, write H(eju). с. d. Find the z-transform of the output, Y(2), when the input is x[n] = u[-n – 1]. Specify the ROC for Y(2). Z-Transform Definition : X(z) A ) «[n]z" n=-00