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iztrans

Inverse Z transform

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MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

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:

f(k)=12πi|z|=RF(z)zk1dz,k=0,1,2...

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

Identifier or indexed identifier

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.

Overloaded By

F

See Also

MuPAD Functions

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