ECE438 Week9 Quiz Question5 Solution
a. System impulse response is the system output when input is impulse signal.
Let
$ x[n]=\delta [n] $
Then
$ \begin{align} h[n]&=\frac{1}{M_1+M_2+1}\sum_{k=-M_1}^{M_2}\delta[n-k] \end{align} $
$ h[n]=\left\{\begin{array}{ll}\frac{1}{M_1+M_2+1}, & -M_1\le n\le M_2 \\ 0, & otherwise \end{array}\right. $
