BUILT-IN MATHEMATICA SYMBOL

InverseZTransform

gives the inverse Z transform of expr.

InverseZTransform

gives the multiple inverse Z transform of expr.

MORE INFORMATION

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

In TraditionalForm, InverseZTransform is output using .

EXAMPLES

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Basic Examples (2)

Univariate inverse transforms:

Multivariate inverse transforms:

Univariate inverse transforms:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Multivariate inverse transforms:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

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:

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 (5)

ZTransform is the inverse operator:

Linearity:

Shifting:

Derivatives:

Initial value property:

Final value property:

InverseZTransform is closely related to SeriesCoefficient:

Neat Examples (1)

Inverse transform for a hypergeometric function: