Inverse bilateral Z transform of a rational function defined in an annulus:

Compute the inverse transform at a single point:

Function defined in the exterior of a disk:

Function defined in the interior of a disk:

Function with an essential singularity at zero:

Multivariate inverse bilateral transform:

Shifted impulse sequences:

Rational functions yield exponential and trigonometric sequences:

Functions involving parameters:

The following function defined in the interior of a circle leads to a trigonometric sequence:

If the ROC is not provided, then it is assumed to be the region containing all the function poles:

Obtain the same result using InverseZTransform:

Calculate the inverse bilateral Z transform at a single point using a numerical method:

Alternatively, calculate inverse symbolically:

Then evaluate it for a specific value of :

For some functions, the inverse bilateral Z transform can be evaluated only numerically:

Plot the inverse bilateral Z transform using numerical values only:

Define finite duration and exponentially decaying signals:

Plot signals in the time domain:

To find the convolution, first calculate product of the transforms:

Then, perform inversion back to the time domain:

Plot the convolution in the time domain:

Alternatively, find the convolution using DiscreteConvolve:

Define a pair of infinite duration signals:

Plot the signals in the time domain:

To find the convolution, first calculate the product of the transforms:

Perform inversion back to the time domain:

Plot the convolution in the time domain:

Alternatively, find the convolution using DiscreteConvolve:

Relation to BilateralZTransform:

InverseBilateralZTransform is closely related to InverseFourierSequenceTransform:

Linearity:

Scaling:

No poles are allowed in the region of convergence:

Create a table of basic inverse bilateral Z transforms: