Question
Asked Dec 2, 2019
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What will be the Laplace transform of x(t)=e--btu(t) with b>0. u(t) is the unit step function.

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Expert Answer

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Step 1

Laplace transform is used to convert any signal from time (t) domain into complex frequency (s) domain. For any function x(t), the Laplace transform of x(t) is defined as

(s)x()edt
> (1)
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(s)x()edt > (1)

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Step 2

The unit step function u(t) is defined as follows:

(1 when t 20
u(t)=
|0 when t <0
->(2)
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(1 when t 20 u(t)= |0 when t <0 ->(2)

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Step 3

In this case, the expression of the function x(t) is given as

...
-bt
x(t) e"u()
> (3)
where b 0
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-bt x(t) e"u() > (3) where b 0

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Electrical Engineering

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