When I was first introduced to convolution, I thought of it as an impulse with an amplitude of 1. This made it easier for me to comprehend the fact that convolving any arbitrary function x(t) with an impulse function returns back the function itself.
That is, if we have: y(t)=x(t)*δ(t); where * is convolution
and we are interested in the value at t=t1, then y(t1)=x(t1).1 ; where . is multiplication
this is because, δ(t1-T) is 0 everywhere except for t=t1, it is equal to 1.
However, I don't know how to reconcile with the fact that the impulse function doesn't have an amplitude of 1, but instead infinity. If so, then by the same logic: y(t1)=x(t1).∞=∞
Can someone, point me to what I am missing? Thank you