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]].