I am learning about discrete systems and in this derivation something struck me as quite odd. Solving for $A_0$ in this equation seems dubious as it ignored all other values of $n$. For example, at $n=-N$ would you not find that $A_0=b_0$? Why does it work for using a single value of n, but ignoring all others? I have been trying to figure out what makes using $n=0$ so special but I don't understand.
Can anyone else help me grasp this? preferably intuitively