Definition

δ(kk0)=δkk0={0for kk01for k=k0\delta(k-k_0) = \delta_{kk_0} = \begin{cases} 0 \quad \text{for } k \neq k_0 \\ 1 \quad \text{for } k = k_0 \end{cases}

Applications

Sifting property:
Sifting property#Discrete form

See also: discrete step function

discrete step function#Relationship between discrete delta, step, delta response, step response