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ECE2260F09_HW5p1asoln

# ECE2260F09_HW5p1asoln - form of f t − τ f t − τ = e...

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2260 F 09 HOMEWORK #5 prob 1a solution E X : Find the Laplace transform of the following waveform: f ( t ) = e a ( t −τ ) u ( t − τ ) where τ > 0 S OL ' N : Use the identity for signals with a delayed turn-on and which are shifted in time: L f ( t a ) u ( t a ) { } = e as F ( s ) , a > 0 where F ( s ) L f ( t ) { } f ( t ) e st dt 0 From the step function, u t − τ ( ) , we identify τ as the value of a . To use the identity, we must identify f ( t − τ ) . The exponential is already in the
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Unformatted text preview: form of f ( t − τ ) : f ( t − τ ) = e − a ( t −τ ) For the delay identity, we need f ( t ) . We obtain f ( t ) by replacing t − τ with t . f ( t ) = e − at We lookup the Laplace transform of e − at in a table: L e − at { } = 1 s + a Our final result: L e − a ( t −τ ) u ( t − τ ) { } = e −τ s ⋅ 1 s + a...
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