# Impulse response of discrete time system

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

• I think showing the full problem might help some. – mark leeds Mar 18 '19 at 1:26