Laplace transform convolution

  • #1

Homework Statement


[itex]x(t) = cos(3πt)[/itex]
[itex]h(t) = e-2tu(t)[/itex]

Find [itex]y(t) = x(t) * h(t) [/itex](ie convolution)

Homework Equations


Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s)

The Attempt at a Solution


[itex] L(x(t)) = \frac{s}{s^2+9π^2} [/itex]
[itex] L(h(t)) = \frac{1}{s+2} [/itex]

I then try to find the partial fractions but it looks more complicated than it should be..
 

Answers and Replies

  • #2
BvU
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What about u(t) ?
 
  • #3
LCKurtz
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Homework Statement


[itex]x(t) = cos(3πt)[/itex]
[itex]h(t) = e-2tu(t)[/itex]

Find [itex]y(t) = x(t) * h(t) [/itex](ie convolution)

Homework Equations


Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s)

The Attempt at a Solution


[itex] L(x(t)) = \frac{s}{s^2+9π^2} [/itex]
[itex] L(h(t)) = \frac{1}{s+2} [/itex]

I then try to find the partial fractions but it looks more complicated than it should be..

Show us your partial fractions work. It shouldn't be all that hard.
 

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