In digital signal processing, a unit delay is a system that delays the input signal by one sample period:
$
y(n) = x(n-1)
$
Computing the [[z-transform]] on both sides:
$
Y(z) = z^{-1} X(z)
$
The unit delay is often represented by a shift register in the time domain or by multiplication by $z^{-1}$ in the z-domain.
![[unit-delay.svg]]
The unit delay is a [[causal system]].