Inverse Z-Transform Calculator
Find the discrete sequence from a standard-form Z-transform expression.
Inputs
x[n] value
0.03125000
x[n] =
x[n] = 0.5^n = 0.03125
Step by step
Values used
X(z) form = z/(z-a) → aⁿu[n]; a (base) = 0.5000; Evaluate x[n] at n = = 5
Inverse Z-transform
x[n] = Z⁻¹{X(z)}
x[n] value
= 0.03125000
x[n] =
= x[n] = 0.5^n = 0.03125
How it works
Finds the inverse Z-transform x[n] = Z⁻¹{X(z)} for standard forms. Supported: • Z⁻¹{z/(z-a)} = aⁿ·u[n] • Z⁻¹{az/(z-a)²} = n·aⁿ·u[n] • Z⁻¹{1} = δ[n] • Z⁻¹{z/(z-1)} = u[n] • Z⁻¹{z/(z-1)²} = n·u[n]
Formula
Inverse Z-transform
x[n] = Z⁻¹{X(z)}
- x[n]
- Discrete sequence
- X(z)
- Z-domain transform
Frequently Asked Questions
How do I invert a complex X(z)?
Use partial fraction decomposition to break X(z)/z into simpler terms, then use the standard inverse transform pairs for each term.
What does u[n] mean?
u[n] is the unit step sequence: u[n] = 1 for n ≥ 0, and 0 for n < 0. It indicates the sequence is causal (right-sided).