# Kronecker Delta Function

The Kronecker Delta Function is given by $δ_{ij}={01 i=ji=j $

From MATH213:

Definition 1: Kronecker delta

The Kronecker delta function $δ[t]$ is defined as the function from $Z$ to ${0,1}$ given by

$δ[t]={10 t=0else $

Theorem 2

For all functions $f:Z→C$, $f[t]=∑_{τ=−∞}f[τ]δ[τ−t]$

Theorem 2 shows how to decompose every function $f$ into a linear combination of impulse functions (i.e. ${δ[τ−t]∣τ∈Z}$ is a basis for all DT functions.)

### From CS370

They use a slightly different notation

$δ_{k,l}={01 k=lk=l $