Howtosignalprocessing
A system is called linear if it has two mathematical properties: homogeneity (hōma-gen-ā-ity) and additivity. If you can show that a system has both properties, then you have proven that the system is linear.
- What are the conditions for a system to be linear?
- What defines a linear system?
- What are the 2 characteristics of a linear system that enables the decomposition of a signal?
What are the conditions for a system to be 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.)
What defines a linear system?
Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up. Linear systems are used to describe both static and dynamic relations between variables.
What are the 2 characteristics of a linear system that enables the decomposition of a signal?
Superposition: Systems that satisfy both homogeneity and additivity are considered to be linear systems. These two rules, taken together, are often referred to as the principle of superposition.
