I basically need to know how to test a system to see if it is linear or not. The professor gave us a "recipe" to check a system. I can kinda follow the recipe, but I would like to understand it, so I have reached out to other sources. The other sources deal with operators from the beginning... thus, I am trying to understand them. The following simple example is throwing me for a loop.(adsbygoogle = window.adsbygoogle || []).push({});

Question:

Determine if the following system is linear.

[tex] y(t) = x(t-2) + x(2-t) [/tex]

Answer:

A system is linear if:

[tex] H \{ \alpha x_1 +\beta x_2 \} = \alpha H\{ x_1 \} + \alpha H\{ x_2 \} [/tex]

I have the solution (the answer is yes - linear), however I do not understand it. What is [tex] H\{ \} [/tex] in this case?

It makes sense to me in examples such as:

[tex] y(t) = \sin(t)x(t) [/tex] so [itex] \sin(t) [/itex] is acting on the input [itex] x(t) [/itex]. But... what is acting on the input here (the x(t-2) + x(2-t) example)?

In words I imagine [itex] H [/itex] to be something that yields an ouput by adding a shifted input to a shifted input. I'm kinda lost... guidance would be helpful.

thanks !

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# Homework Help: Linear System - need some help

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