Part C: Linearity

My definition of linearity in terms of systems is:

A system whose output combined with a linear shift is equivalent to the output if the linear shift is on the input of the system.


An example of a linear system is:

$ x(t) = t + 3 $

To prove this:

$ Y_1(t) = A*x(t) = Z_1(t) $

$ Y_2(t) = X(At) = Z_2(t) $

$ Z_1(t) = Z_2(t) $

for any number A

Non-linear

$ x(t) = t^2 $

Is an example of a non linear system. The order of linear operations before and after the system affect the result of the cascade

for t = 2 and A = 2 $ Y_1(2) = 2*x(2) = 8 $

$ Y_2(2) = x(2*2) = 16 $

$ Z_1(t) \neq Z_2(t) $

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