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Engineering and Tech / Signals and Systems 2 / Chapter 9 / Problem 9.21

Signals and Systems | 2nd Edition | ISBN: 9780138147570 | Authors: Alan V. Oppenheim, Alan S. Willsky, with S. Hamid

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Determine the Laplace transform and the associated region of convergence and polezero

Chapter 9, Problem 9.21

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QUESTION:

Determine the Laplace transform and the associated region of convergence and polezero plot for each of the following functions of time: (a) x(t) = e- 21 u(t) + e- 31 u(t) (b) x(t) = e-41 u(t) + e- 51 (sin5t)u(t) (c) x(t) = e21 u(-t)+e31 u(-t) (d) x(t) = te-21tl (e) x(t) = ltle-2ltl (0 x(t) = ltle2t u( -t) { 1 O:St:S (g) x(t) = o: elsewhere { t 0:St:S1 (h) x(t) = 2 - t, 1 :S t :S 2 (i) x(t) = o(t) + u(t) (j) x(t) = o(3t) + u(3t)

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QUESTION:

Determine the Laplace transform and the associated region of convergence and polezero plot for each of the following functions of time: (a) x(t) = e- 21 u(t) + e- 31 u(t) (b) x(t) = e-41 u(t) + e- 51 (sin5t)u(t) (c) x(t) = e21 u(-t)+e31 u(-t) (d) x(t) = te-21tl (e) x(t) = ltle-2ltl (0 x(t) = ltle2t u( -t) { 1 O:St:S (g) x(t) = o: elsewhere { t 0:St:S1 (h) x(t) = 2 - t, 1 :S t :S 2 (i) x(t) = o(t) + u(t) (j) x(t) = o(3t) + u(3t)

ANSWER:

Step 1 of 20

Part (a)

The expression is given as,

Apply the Laplace transform to the above function.

Solve further as

Hence, the region of the conversion ROC is , and the Laplace transform of the system is .

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