Digital delay

A digital delay line is a discrete element in digital filter theory, which allows a signal to be delayed by a number of samples. If the delay is an integer multiple of samples, digital delay lines are often implemented as circular buffers. This means that integer delays can be computed very efficiently.

The delay by one sample is notated ${\displaystyle \mathrm {z} ^{-1}}$ and delays of ${\displaystyle N}$ samples is notated as ${\displaystyle \mathrm {z} ^{-N}}$ motivated by the role the z-transform plays in describing digital filter structures.

...
Wikipedia