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Determine the z-transform for each of the following sequences. Sketch the polezero plot
Chapter 10, Problem 10.21(choose chapter or problem)
Determine the z-transform for each of the following sequences. Sketch the polezero plot and indicate the region of convergence. Indicate whether or not the Fourier transform of the sequence exists. (a) S[n + 5] (b) S[n- 5] (c) ( -l)nu[n] (d) C4Y+ 1 u[n + 3] (e) (-~)nu[-n- 2] (0 Ci)nu[3- n] (g) 2nu[ -n] + (i)nu[n- 1] (h) (~)n- u[n- 2]
Questions & Answers
QUESTION:
Determine the z-transform for each of the following sequences. Sketch the polezero plot and indicate the region of convergence. Indicate whether or not the Fourier transform of the sequence exists. (a) S[n + 5] (b) S[n- 5] (c) ( -l)nu[n] (d) C4Y+ 1 u[n + 3] (e) (-~)nu[-n- 2] (0 Ci)nu[3- n] (g) 2nu[ -n] + (i)nu[n- 1] (h) (~)n- u[n- 2]
ANSWER:Step 1 of 8
(a)
Consider the following sequence:
Apply z-transform to the sequence.
is impulse sequence defined at
Hence
Hence the z-transform of is,
The sequence converges for all values of . Hence region of convergence (ROC) is all z, except .
Since ROC includes a unit circle , hence, has a Fourier transform.
The pole-zero plot is,