Sifting property

Continuous form

see δ-function, sifting property states $$f(\tau)=\int_{-\infty}^\infty f(\lambda) \delta (\tau - \lambda) d \lambda$$

arbitrary function expressed as linear combination of $\delta$ functions

Discrete form

expressing an arbitrary discrete function as a linear combination of discrete delta functions: $$f(k) = \sum_{i=-\infty}^\infty f(i) \delta(k-i)$$