High pass filter and signal
I have this problem about signal that I have a little trouble to finish:
I attached a small figure of the circuit.
I have a High pass filter, and the equation is:
the solution for the equation is:
This is what I found and it matches with the answer from the professor.
But the question said:
Find the solution of the ODE to obtain y[t] as some integral of x[t].
Now I need to take away the and replace by .
What i did is to use the integration by part to the solution .
My problem is that by intergrating, even though I took away what I wanted, I have introduced the variable t. I dont know if it is a problem.
My second question is the following:
Find the impulse response function so that the solution is has the form:
Hint: if you find a lonely x(t), remenber that:
Here I am confused with the boundaries of the integration
Please can I have some help with the problem