kronecker delta function

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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}
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