This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# InverseZTransform

 InverseZTransformgives the inverse Z transform of expr. InverseZTransformgives the multiple inverse Z transform of expr.
• The inverse Z transform of a function is given by the contour integral .
• The multidimensional inverse Z transform is given by .
• The following options can be given:
 Assumptions \$Assumptions assumptions to make about parameters Method Automatic method to use
Univariate inverse transforms:
Multivariate inverse transforms:
Univariate inverse transforms:
 Out[1]=
 Out[2]=

Multivariate inverse transforms:
 Out[1]=
 Out[2]=
 Scope   (4)
Shifted impulse sequence:
Rational transforms yield exponential and trigonometric sequences:
In some cases additional simplification and transformations are needed:
Elementary functions:
Special functions:
 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:
ZTransform is the inverse operator:
Linearity:
Shifting:
Derivatives:
Initial value property:
Final value property:
InverseZTransform is closely related to SeriesCoefficient:
Inverse transform for a hypergeometric function: