Determining if a system is Linear

To determine if a system is linear, we need to answer the following question: When an input signal is applied to the system, does the output response exhibit homogeneity and additivity? If a system is both homogeneous and additive, it is a linear system.

1. How do you find the linearity of a system example?
2. What makes a system linear?
3. How do you prove that a system is not linear?
4. What are the 2 conditions for a system to be linear?

How do you find the linearity of a system example?

System is said to be linear if it satisfies these two conditions: Superposition - if input applied is (x1+x2), then the output obtained will be y1+y2 . (equivalently we say that if x1 and x2 are applied simultaneously then out put will be the sum of the outputs obtained individually)

What makes a system linear?

A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties, without restrictions (that is, for all inputs, all scaling constants and all time.)

How do you prove that a system is not linear?

Generally, if the equation describing the system contains square or higher order terms of input/output or product of input/output and its derivatives or a constant, the system will be a non-linear system. Triangulation of GPS signals is an example of non-linear system.

What are the 2 conditions for a system to be linear?

► A system is called linear if it has two mathematical properties: homogeneity and additivity.