1. Consider the z-transform X(z) whose pole-zero plot is shown below. a) Determine the ROC if it is known that the Fourier transform exists. For this case, determine whether the corresponding sequence is right-sided, left-sided, or two-sided. b) How many possible two-sided sequences have the pole zero plot shown below? c) Is it possible for the pole-zero plot to be associated with a sequence that is both stable and causal? If so, give the appropriate region of convergence. Im unit circle 0.5 1.5 3.0 Re

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1. Consider the z-transform X(z) whose pole-zero plot is shown below.
a) Determine the ROC if it is known that the Fourier transform exists. For this case, determine whether
the corresponding sequence is right-sided, left-sided, or two-sided.
b) How many possible two-sided sequences have the pole zero plot shown below?
c) Is it possible for the pole-zero plot to be associated with a sequence that is both stable and causal?
If so, give the appropriate region of convergence.
Im
unit circle
0.5
1.5
3.0
Re
Transcribed Image Text:1. Consider the z-transform X(z) whose pole-zero plot is shown below. a) Determine the ROC if it is known that the Fourier transform exists. For this case, determine whether the corresponding sequence is right-sided, left-sided, or two-sided. b) How many possible two-sided sequences have the pole zero plot shown below? c) Is it possible for the pole-zero plot to be associated with a sequence that is both stable and causal? If so, give the appropriate region of convergence. Im unit circle 0.5 1.5 3.0 Re
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