kronecker delta function
Table of Contents
Delta function denoting an impulse.
In the context of discrete signals, the sample function \(\delta[n]\) denotes the value \(\delta_{n0}\) where
\begin{equation}
\delta_{ij} =
\begin{cases}
0 & i \neq j \\
1 & i = j \\
\end{cases}
\end{equation}
Also see the dirac delta function.
So, \(\delta[n-k]\) denotes a 1 where \(n=k\).
1. Sifting property
\begin{equation}
\sum_{i=\infty}^{\infty} a_i \delta_{ij} = a_j
\end{equation}