Find the discrete sequence from a standard-form Z-transform expression.
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]
Inverse Z-transform
x[n] = Z⁻¹{X(z)}
Use partial fraction decomposition to break X(z)/z into simpler terms, then use the standard inverse transform pairs for each term.
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).