Delta Operator - Examples

Examples

• The forward difference operator

is a delta operator.

• Differentiation with respect to x, written as D, is also a delta operator.

• Any operator of the form

(where Dn(ƒ) = ƒ(n) is the nth derivative) with is a delta operator. It can be shown that all delta operators can be written in this form. For example, the difference operator given above can be expanded as

• The generalized derivative of time scale calculus which unifies the forward difference operator with the derivative of standard calculus is a delta operator.

• In computer science and cybernetics, the term "discrete-time delta operator" (δ) is generally taken to mean a difference operator

the Euler approximation of the usual derivative with a discrete sample time . The delta-formulation obtains a significant number of numerical advantages compared to the shift-operator at fast sampling.