Define an exponentially decaying sequence:

Compute its bilateral Z transform:

Complex plot of the bilateral Z transform:

Compute the transform at a single point:

Compute the bilateral Z transform of a multivariate function:

Bilateral Z transform of the UnitStep function:

Discrete power function:

Combination of power functions:

DiscreteDelta:

Discrete-time, finite support function:

Trigonometric sequence:

Calculate the bilateral Z transform at a single point:

Alternatively, calculate the transform symbolically:

Then evaluate it for a specific value of :

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

Plot the bilateral Z transform using numerical values only:

Define finite duration signals:

Plot the signals in the time domain:

To find the convolution, first calculate the 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 infinite duration signals:

Plot the signals in the time domain:

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

Perform the inversion back to the time domain:

Plot the convolution in the time domain:

Alternatively, find the convolution using DiscreteConvolve:

BilateralZTransform and InverseBilateralZTransform are mutual inverses:

BilateralZTransform is closely related to FourierSequenceTransform:

Linearity:

Time shifting:

Scaling in the -domain:

Convolution:

Differentiation in the -domain: