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Linear Systems

A linear system is defined as a system that if two inputs were placed in parallel into a system and then summed yields the same result as adding two inputs together and then placed into that system.

In another form, it may be translated as:

Parallel: A -> SYSTEM -> C B -> SYSTEM -> D

where the resulting sum is C+D.

Sum: A+B -> SYSTEM -> C+D.

Example of Linear System

$ x(t) -> SYSTEM -> y(t) \ $

$ w(t) -> SYSTEM -> z(t) \ $

with sum equaling $ y(t)+z(t) \ $

$ x(t) + w(t) -> SYSTEM -> y(t)+z(t) \ $

If $ x(t) = t \ $ and $ w(t) = t^2 \ $, and the SYSTEM multiplies any input $ x(t) \ $ and multiplies it by 2 and any input $ w(t) \ $ and multiplies by 3, then the result $ y(t)+z(t) \ $ would equal $ 2*x(t)+3*w(t) \ $ for both parallel, system-passed and then summed as well as summed then system-passed methods.

Example of Nonlinear System

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva