CHAPTER 1

Linear Systems Theory

Characterizing the complete input-output properties of a system by exhaustive measurement is usually impossible. When a system qualifies as a linear system, it is possible to use the responses to a small set of inputs to predict the response to any possible input. This can save the scientist enormous amounts of work, and makes it possible to characterize the system completely. (Professor David Heeger)

To see whether a system is linear, we need to test whether it obeys certain rules that all linear systems obey. The two basic tests of linearity are homogeneity and additivity.

• Homogeneity: As we increase the strength of a simple input to a linear system, say we double it, then we predict that the output function will also be doubled.

• Additivity: If a single input is given separately and the result of these two separate inputs is equal to the input as whole, then it is said to be in a linear system.

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