Frequency Response of an analog system?

[paulie walnut]

An input of 2.δ(t) is applied to a system and produces the response

y(t)=6.e^-2t - 4.e^-3t

Find an expression for the systems frequency response. The method used would be great too. I know there's some Fourier transforms involved.

 

[profase]

You know x(t) and y(t). It's also assumed that it's a linear system. Therefore,
y(t) = x(t) * h(t) (* = convolution)
Also, remember that convolution in one domain (eg time domain) is multiplication in the other domain (eg frequency domain). Therefore,
Y(jw) = X(jw) * H(jw) (* = multiplication)

So there are two ways you can attack this. You can either find h(t) (which is relatively straightforward) and then find the transform of that, or you can find the transforms of y(t) and x(t), and then solved for H(jw).

Hope that helps,
John