Exam1 question 3.
An LTI system has unit impulse response $ h[n] = u[-n] $. compute the system's response to the input $ x[n]=2^nu[-n] $. (Simplify your answer until all $ \sum $ signs disappear.)
Solution
$ y[n] = x[n] * h[n]\! $
$ =\sum_{k=-\infty}^{\infty} x[k]h[n-k] $
$ =\sum_{k=-\infty}^{\infty} 2^{k}u[-k]u[-(n-k)] $
$ =\sum_{k=-\infty}^{0}2^{k}u[-u+k] $
