Basic question about Laplace and signals properties

[tamtam402]

Hey guys, I have a butterworth high-pass filter, and I was asked to find it's temporal response equation to the u(t) function. That part was easy, using basic Laplace tables I was able to find the following equation:
y(t)=√2 e^(-31100t) *cos⁡(31000t+π/4)u(t)
However, I'm supposed to be able to use that result to find the output equation (in the time domain) for a constant signal of magnitude 1V from 0 to 0.5ms, and 0V from 0.5 to 1ms. I'm at a loss here, because when using simulink (in Matlab) to simulate the response, I see that the output "responds" to the 1V to 0V transition. That means I can't simply use my equation with u(t) = 1 for t = 0 to 0.5ms, and u(t) = 0 for t = 0.5 to 1ms. What am I supposed to do?

 

[pghaffari]

I would help you, but I'm signed up to take my first signals class next quarter!

Sorry!

Doesn't time domain mean just convert it from phasors to regular coordinates? but you already have it in terms of t so yah I wouldn't be able to help you yet :|

 

[pylauzier]

Ok I found out how to solve the problem. Using the superposition principle, substract 2 step functions to generate a pulse only for the first 0.0005 seconds. Do the same thing on the output.