The basic idea behind the Z-transform is same to Laplace, and it was re-introduced in 1947 by W. Hurewicz and to find a way to treat sampled-data control systems used with radar. It gives a easy way to solve linear, constant-coefficient difference equations. It was later change to "the z-transform" by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952. The idea contained within the Z-transform is also known in mathematics as the method of creating functions which can be turned back to its original form as early as 1730 when it was introduced by de Moivre along with probability theory. From a mathematical view the Z-transform can also be seen as a Laurent series where one views the sequence of numbers under consideration as the (Laurent) expansion of an analytic function.

MATLAB facilitates in solving Z-transforms problems like Z-Transform of Symbolic Expression, Specify Independent Variable and Transformation Variable, Z-Transforms Involving Dirac and Heaviside Functions, Z-Transform of Array Inputs, Z-Transform of Symbolic Function with the help of below written functions.

## ztrans(f)

finds the Z-Transform of f. By default in MATLAB the independent variable is n and the transformation variable is z. If f does not contain any function n, ztrans uses symvar.

## ztrans(f,transVar)

uitlises the transformation variable transVar instead of z.

## ztrans(f,var,transVar)

finds solution with help of the independent variable var and transformation variable transVar instead of n and z, respectively.