The discussion focuses on solving the convolution of two functions, x(t) = cos(3πt) and h(t) = e-2tu(t), using Laplace transforms. The Laplace transforms are given as L(x(t)) = s/(s2 + 9π2) and L(h(t)) = 1/(s + 2). The convolution theorem states that Y(s) = X(s)H(s), leading to the need for partial fraction decomposition to simplify the expression before taking the inverse Laplace transform.
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redundant6939 said:Homework Statement
x(t) = cos(3πt)
h(t) = e<sup>-2t</sup>u(t)
Find y(t) = x(t) * h(t)(ie convolution)
Homework Equations
Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s)
The Attempt at a Solution
L(x(t)) = \frac{s}{s^2+9π^2}
L(h(t)) = \frac{1}{s+2}
I then try to find the partial fractions but it looks more complicated than it should be..