The question is x(t) = t
h(t) = 2δ(t-1)
I am supposed to find y(t)

so I end up with the integral from -infinity to infinity of 2tδ(t-1)

so I sub in 1 into t giving me 2.

However, my lecturer say the answer is 2t-2

 

This is not a problem of sustitution, It is a problem of integration by parts

 

Hello hitmen,

Impulse response is the response we get when we give an input signal of magnitude 1 at t=0.
Here the response is 2del(t-1).so the magnitude is 2 times the input(as we gave a signal of magnitude 1) and it is delayed in time by 1 (t-1).

So whatever signal we give it is delayed in time by 1 and its magnitude becomes 2 times.

so t is delayed by 1 and hence t-1 and magnitude becomes twice and so 2(t-1).

Hope this helps