InverseZTransform

InverseZTransform[expr,z,n]

gives the inverse Z transform of expr.

InverseZTransform[expr,{z1,,zm},{n1,,nm}]

gives the multiple inverse Z transform of expr.

Details and Options

• 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:

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:

Linearity:

Shifting:

Derivatives:

Initial value property:

Final value property:

InverseZTransform is closely related to SeriesCoefficient:

Neat Examples(1)

Inverse transform for a hypergeometric function:

Wolfram Research (1999), InverseZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseZTransform.html (updated 2008).

Text

Wolfram Research (1999), InverseZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseZTransform.html (updated 2008).

CMS

Wolfram Language. 1999. "InverseZTransform." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/InverseZTransform.html.

APA

Wolfram Language. (1999). InverseZTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseZTransform.html

BibTeX

@misc{reference.wolfram_2024_inverseztransform, author="Wolfram Research", title="{InverseZTransform}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/InverseZTransform.html}", note=[Accessed: 25-June-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_inverseztransform, organization={Wolfram Research}, title={InverseZTransform}, year={2008}, url={https://reference.wolfram.com/language/ref/InverseZTransform.html}, note=[Accessed: 25-June-2024 ]}