EECS20N: Signals and Systems


In a state machine, the variable n denotes the step. The real time between two steps is not necessary fixed. Many of the infinite-state systems we will consider, however, are discrete-time systems, where the real time between two steps is fixed, say at δ seconds. In this case, step n occurs at seconds.

If the time index represents real time, then it may not make much sense to allow stuttering. Real time advances relentlessly, and physical quantities have values at all points in real time. Hence, we will often disallow stuttering inputs and outputs for discrete-time systems.

If the update function does not change with the time index, then the system is said to be time invariant.