# Why is the unit step function in the end is written as $u(t-t_1-t_0)$ instead of just $u(t-t_0)$?

So this is basically about signals and systems and how to compute the output of the system using only the impulse response and the given input signal- where x(t) is the input signal and h(t) is the impulse response. the output y(t) is simply the convolution of the impulse response and input. At first it's all good as convolution is applied. I get how the limits of integration are changed accordingly because of the two unit step functions. and then I'm stuck.

f(T) in the picture below is supposed to be x(t). thanks in advance

• Look at the limits of integration. – amd Apr 20 at 18:34
• Now that you said it, I noticed that in all the problems I solved, I could just put the upper limit - the lower limit inside the argument of the unit step function and it works. I gotta say, though, I never did it this way before, because I was able to draw and see what happens- and thus deduce what unit function should be written next to the integral evaluation. In this case it was a bit tricky to draw and see what happens, so I guess I'll just take what u said as a rule of thumb. – Sami Sawani Apr 20 at 18:56