If we know that a delta function $([n]$ as an input to an LSI system results in an output of $h[n],$ what is the output of the following LSI system?

${\displaystyle \underset{k=-}{\overset{}{}}}{a}_k[n-k]$

Linear Shift$-$Invariant System

$9.$ Write the decomposition of a infinitely long general sequence $x[n]$ into a sum of weighted and shifted delta functions $([n]).$

$10.$ If we know that a delta function $([n])$ as an input to an LSI system results in an output of $h[n],$ what is the output of an LSI system with your decomposed general sequence from question $9$ as the input?

Answer all