Find Y(s)/X(s) for y(t) = u(t - a).x(t)

[Debdut]

y(t) = u(t - a) . x(t)
u(t) is a unit step function. I have to find Y(s)/X(s). Do I have to do convolution in frequency domain?

 

[HallsofIvy]

First, are we to assume that "X(s)" and "Y(s)" are the Laplace transforms of x(t) and y(t)? I don't see any reason why you just cannot calculate directly that the Laplace transform of y(t) is e^{-s}X(s) or get it from a table of transforms.

 

[Debdut]

Thanks for the quick reply.
Do you mean e^-asX(s). But that is the laplace of x(t - a).
Am I wrong?

 

[Debdut]

Found an article where they're saying Y(s) should be Y(s) = e^-as . Laplace{x(t + a)}