Quiz6Soln - Name ECE 301 Quiz 6 Purdue University Summer 2009 1 Let x(t = et u(t for some complex number Find Lcfw_x(t = x(t)est dt along with its

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Name: ECE 301: Quiz 6 Purdue University, Summer 2009 1. Let x ( t ) = e - αt u ( t ), for some complex number α . Find L{ x ( t ) } = i -∞ x ( t ) e - st dt , along with its region of convergence (ROC). Hint: The ROC is the set of s for which the integral converges. Solution: L{ x ( t ) } = I -∞ x ( t ) e - st dt = I -∞ e - αt u ( t ) e - st dt = I 0 e - t ( α + s ) dt = b e - t ( α + s ) - ( α + s ) B t =0 Note that if R { s } < - R { α } , then lim t →∞ e - t ( α + s ) = . Therefore the ROC is R { s } > - R { α } , and for s in the ROC, X ( s ) = L{ x ( t ) } = 1 s + α . 2. Using the answer from Problem 1, ±nd x ( t ) if
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This note was uploaded on 03/30/2011 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue University-West Lafayette.

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