Linearity

• A system is called linear if the following holds:
  • Let s₁(t) be the input to the system, and denote by v₁(t) the resulting output.
  • Then, let s₂(t) be the input to the system, and denote by v₂(t) the resulting output.
  • Then form the combination of input signals a₁ s₁(t)+a₂ s₂(t) and use it as an input to the system.
  • The system is called linear if the resulting output is a₁ v₁(t)+a₂ v₂(t)
• Note: This condition must hold for any s₁(t), s₂(t), a₁, and a₂ for the system to be linear.
• We say, that for a linear system superposition holds.
• Example: The RC-circuit investigated in the lab (Lab 4) is linear.