Reference no: EM13891693
1. Determine the Z-transform and the corresponding ROC of x[n] = αnu[n + 1] + βnu[n + 2] where |β| > |α| > 0. Show its pole-zero plots and indicate clearly the ROC in the plot.
2. Determine the Z-transform and the corresponding ROC of x[n] = αnu[n- 2] + βnu[-n- 1] where |β| > |α| > 0. Show its pole-zero plots and indicate clearly the ROC in the plot.
3. Determine the Z-transform and the corresponding ROC of y[n] = n2αnu[n].
4. Determine the Inverse Z-transform of X(Z) = 7+3.6Z-1/1+0.9Z-1+0.18Z-2. Assume that the sequence x[n] is causal (right-sided).
5. The Z-transform of a right-sided sequence h[n] is: H(Z) = Z+1.7/(Z+0.3)(Z-0.5). Find its Inverse Z-transform h[n].
6. Consider the digital filter structure shown below, where H1(Z) = 2.1 + 3.3Z-1 + 0.7Z-2, H2(Z) = 1.4 - 5.2Z-1 + 0.8Z-2, and H3(Z) = 3.2 + 4.5Z-1 + 0.9Z-2. Determine the overall system transfer function H(Z).
7. A causal LTIV discrete-time system is described by the difference equation: y[n] = 0.4y[n - 1] + 0.05y[n - 2] + 3x[n], where x[n] and y[n] are, respectively, the input and the output sequences of the system.
(a) Determine the transfer function H(Z) of the system.
(b) Determine the impulse response h[n] of the system.
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: A causal LTIV discrete-time system is described by the difference equation: y[n] = 0.4y[n - 1] + 0.05y[n - 2] + 3x[n], where x[n] and y[n] are, respectively, the input and the output sequences of the system. Determine the transfer function H(Z) of ..
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