Unit Delay in Z Domain

If the discrete-time system has an impulse response that is delayed by a single timestep, by following the equation
$$Y(z)=\sum_{n=0}^\infty y[n]z^{-n}=0\cdot z^{-0}+1\cdot z^{-1}+0\cdot z^{-2}+0\cdot z^{-3}+…$$
We can see that a unit delay is equal to $z^{-1}$. Therefore a delay of $n$ samples is $z^{-n}$

Pilot-Induced Oscillations – can be caused by time delays in digital flight control systems

Sources

• “Understanding the Z-Transform – YouTube.” Accessed: May 13, 2023. [Online]. Available: https://www.youtube.com/

Backlinks

[[Laplace Transform of a Time Delay]]
[[Z-Domain]]