ECE2260F09_HW5p2soln

ECE2260F09_HW5p2soln - L { f ( at )} = f ( ) e s a d a = 1...

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2260 F 09 Homework #5 prob 2 solution I DENTITY : L { f ( at )} = 1 a F s a for a > 0 P ROOF : By definition, we have the following equation: L { f ( at )} = f ( at ) e st dt 0 We change variables to τ = at . At t = 0 , τ = a 0 = 0 . For t -> , τ = a = . Inside the integral, st = s τ / a . For dt we have d τ / dt = a , so dt = d τ / a . Making these substitutions, our identity is verified:
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Unformatted text preview: L { f ( at )} = f ( ) e s a d a = 1 a f ( ) e s a d = 1 a F s a . N OTE : is a variable of integration that we may replace with t in the final integral....
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This document was uploaded on 09/02/2010.

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