gives the inverse Z transform of expr.


gives the multiple inverse Z transform of expr.

Details and Options


open allclose all

Basic Examples  (2)

Univariate inverse transforms:

Multivariate inverse transforms:

Scope  (4)

Constants lead to impulse sequences:

Shifted impulse sequence:

Rational transforms yield exponential and trigonometric sequences:

In some cases, additional simplification and transformations are needed:

Elementary functions:

Special functions:

Options  (1)

Assumptions  (1)

This transform will not evaluate without any constraints on the range of p:

Use Assumptions to limit the range of p:

Applications  (3)

Solve a linear difference equation:

Add an initial value equation and solve the algebraic equation for the transform:

Get the solution through inverse transformation:

Use RSolve:

Solve a linear difference-summation equation:

Use the inverse transform to get a solution to the original problem:

Use RSolve:

A discrete system transfer function:

Impulse response:

Step response:

Ramp response:

Properties & Relations  (6)

Use DiscreteAsymptotic to compute an asymptotic approximation:

ZTransform is the inverse operator:




Initial value property:

Final value property:

InverseZTransform is closely related to SeriesCoefficient:

Neat Examples  (1)

Inverse transform for a hypergeometric function:

Introduced in 1999
Updated in 2008