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16. Given f(t) = 2e-tu(t) + 4u(-t) a) Using the Unilateral Laplace Transform table and the...
Laplace Transform
Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...
7. Consider the following signals f(t) = 4e-2tu(t) _ 2e-tu(t) v(t) = 2e-t/3 sin(5t)u(t) w(t) = te-2tu(t) Which of these signals (if any) (a) has repeated poles? (b) could be the impulse response of an all pass filter? (e) has poles on the ju-axis? (d) has a DC gain of 0? (e) has a left-sided ROC (Re(s) < a)?
Let (t) 2eeu(t). (Recall that u(t) is the unit step function.) Use the Laplace trans- form integral to compute (not look up from a table) this signal's Laplace transform X(s) and find its region of convergence (ROC). Draw a sketch that shows the pole(s) and ROC of X(s)
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Find the Laplace transform of the following signals and in each case determine the corresponding region of convergence: 3.4 (a) (b) the signal x(t)=e-ulu(t)-eatu-t)when (i) α > 0, (ii) α→0, a sampled signal Xi (t) = e (t n) CHAPTER 3: The Laplace Transform (c) the "stairs to heaven" signal (d) the sinusoidal signal r(t) [cos(2(1-1)) + sin(2π1)]a(1-1), (e) the signal y(t)=t2e-21 u(t) using that x(t)=tathasx(s)=2/s. Answers: (a) As α → 0,x(t)...
Find the Laplace transform F(s) L(f(t)) given f(t) = 5e-4 sin(5t) + 2e cos(6t). F(8) =