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Z-Transform (Table Lookup)

Common Z-transforms for discrete-time sequences.

Select sequence
X(z)

Select sequence.

Technical Description & Theory

What is Z-Transform Calculator and Why it Matters?

The Z-transform is the discrete-time counterpart of the Laplace transform, used for difference equations and digital filters.

Mathematical Formula and Theory

X(z)=Σ x[n] z^{−n}. Region of convergence is an annulus in the complex plane.

How to Use This Calculator - Step by Step

  • Select a standard sequence and parameter.
  • Click Transform.

Solved Example with Full Calculation

Z{(0.5)^n u[n]} = z/(z−0.5), |z|>0.5.