Impulse Response Function Problem

[abcz4113]

I attempted by inputting u(τ-t)u(t-τ) into the second part of the integral. Since I want to change the second part of the integral to go from [+∞, -∞]. And as for first part of the integral I added a u(t-τ) term after the x(τ) to change the integral from [t,-∞] into [+∞, -∞]. I am not sure if I did them right. And after factoring out the common term x(τ)u(t-τ) (I assume this is my input) from the two integrals I get that my IRF h(t,τ) = 1 + e^(t-τ) * u(τ-t). I am not sure about the answer and I did not know how to solve for the Unit Step Response of this system. Please Help. Thank you.

 

[jfgobin]

Hello abcz4113,

At first thought, I would separate the cases where $t<0$, $t=0$ and $t>0$, assuming your impulse or unit step happens at $t=0$, and use the knowledge of $h(t)$ and $g(t)$.

I will have a closer look at this in a moment.

 

[rude man]

My first observation is that this system seems to be non-causal. Compare the first integral to the convolution integral relating input to output, then ask yourself what the second integral is doing there ...

 

[abcz4113]

Thank you for your hints. I know how to do it now.