The basic idea known behind the Z-transform was same as known to Laplace, and it was re-introduced in 1947 by W. Hurewicz and to find different way to treat sampled-data control systems used with radar. It provides a simple way to solve linear, constant-coefficient difference equations. It was later changed to "the z-transform" by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952.The advanced Z-transform was later developed and by E. I. Jury. The idea contained within the Z-transform is also known in mathematical area as the method of formation of functions which can be fetch back as early as 1730 when it was introduced by de Moivre along with probability. In different way the Z-transform can be seen as a Laurent series where the sequence of numbers under consideration as the (Laurent) expansion of an analytic function.

In MATLAB inverse z-transform can be calculated with the help of below written functions.

- iztrans(F)
- iztrans(F,transVar)
- iztrans(F,var,transVar)

## iztrans(F)

returns the Inverse Z-Transform of F. By default, in MATLAB the independent variable is z and the transformation variable is n. If F does not contain any function of z, iztrans uses the function symvar.

## iztrans(F,transVar)

this function accept two arguments, the transformation variable transVar instead of n.

## iztrans(F,var,transVar)

this function uses the independent variable var and transformation variable transVar instead of z and n respectively.

MATLAB provides simplified way to solve inverse z-transform like Inverse Z-Transform of Symbolic Expression, Specifying Independent Variable and Transformation Variable, Inverse Z-Transforms Involving Kronecker Delta Function ,Inverse Z-Transform of Array Inputs, Inverse Z-Transform of Symbolic Function.