Time-invariance

• A system is called time-invariant if it does not change with time.
• Specifically, if the input-output relationship does not change with time we say the system is time-invariant.
• For a system to be time-invariant, the following must hold:
  • Let v_in(t) be the input to the system and s_out(t) be the resulting output.
  • Apply the same input again T seconds later, i.e., the input is v_in(t-T).
  • For the system to be time-invariant, the output must be s_out(t-T).
• Again, this property must hold for arbitrary inputs v_in(t) and delays T.
• Example: The RC-circuit investigated in the lab (Lab 4) is time-invariant.
• Example: All operations tabulated above are time-invariant.