Compute the Z-transform of standard discrete sequences from coefficient parameters.
Computes the Z-transform X(z) = Σ x[n]·z⁻ⁿ for standard discrete sequences. Supported transforms: • Z{aⁿu[n]} = z/(z-a), |z|>|a| • Z{n·aⁿu[n]} = az/(z-a)², |z|>|a| • Z{δ[n]} = 1, all z • Z{u[n]} = z/(z-1), |z|>1 • Z{n·u[n]} = z/(z-1)², |z|>1 • Z{sin(ωn)u[n]} = z·sin(ω)/(z²-2z·cos(ω)+1) • Z{cos(ωn)u[n]} = z(z-cos(ω))/(z²-2z·cos(ω)+1)
Z-transform definition
X(z) = Σ x[n]·z^(-n) for n = 0 to ∞
It's the discrete-time equivalent of the Laplace transform, used in digital signal processing and control systems to analyze discrete-time systems.
The ROC defines the values of z for which the Z-transform sum converges. It determines whether the system is causal and stable.