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Inverse Z transform

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iztrans(F, z, k)


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.


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)



Arithmetical expression or matrix of such expressions


Identifier or indexed identifier


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


See Also

MuPAD Functions


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