Given two discrete-time systems and connected in cascade to form a new system , we examine the following properties:
If and are linear, i.e. for all signals and scalars ,
then is also linear
If and are time invariant, i.e. for all signals and integers ,
then is also time invariant
If and are linear and time-invariant, there exists signals and such that for all signals , and , thus
or interchanging and order does not change .
If and are causal, i.e. for all signals , and any choise of integer ,
then is also causal.
If and are stable, i.e. there exists a signal and scalars and that for all integers ,
then is also stable, i.e. there exists a signal and scalars , and that for all integers ,