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iztrans

Inverse Z transform

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

```iztrans(F, z, k)
```

Description

iztrans(F, z, k) computes the inverse Z transform of the expression F = F(z) with respect to the variable z at the point k.

If R is a positive number, such that the function F(Z) is analytic on and outside the circle |z| = R, then the inverse Z-transform is defined as follows:

If iztrans cannot find an explicit representation of the transform, it returns an unevaluated function call. See Example 3.

If F is a matrix, iztrans applies the inverse Z transform to all components of the matrix.

To compute the direct Z transform, use ztrans.

Examples

Example 1

Compute the inverse Z transform of these expressions:

`iztrans(exp(1/z), z, k)`

`iztrans((z*sin(1))/(z^2 - 2*cos(1)*z + 1), z, k)`

Example 2

Compute the inverse Z transform of this expression with respect to the variable z:

`f := iztrans((3*z)/(z - 1) + (2*z)/(z - 1)^2, z, k)`

Evaluate the inverse Z transform of the expression at the points k = 2 a + 3 and k = 1 + i. You can evaluate the resulting expression f using | (or its functional form evalAt):

`f | k = 2*a + 3`

Also, you can evaluate the inverse Z transform at a particular point directly:

`iztrans((3*z)/(z - 1) + (2*z)/(z - 1)^2, z, 1 + I)`

Example 3

If iztrans cannot find an explicit representation of the transform, it returns an unevaluated call:

`iztrans(F(z), z, k)`

ztrans returns the original expression:

`ztrans(%, k, z)`

Example 4

Compute the inverse Z transforms of these expressions. The results involve the kroneckerDelta function:

`iztrans(1/z, z, k)`

`iztrans((z^3 + 3*z^2 + 6*z + 5)/z^5, z, k)`

Example 5

Compute the inverse Z tranform of this expression:

`iztrans(z*diff(g(z), z), z, k)`

Parameters

 F Arithmetical expression or matrix of such expressions z k Arithmetical expression representing the evaluation point

Return Values

Arithmetical expression or unevaluated function call of type iztrans. An explicit result can be a piecewise object. If the first argument is a matrix, then the result is returned as a matrix.

F

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