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Mathematical proof for non linear system

  1. Jan 26, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider the continuous-time processing system in figure 1, which has two inputs and one output. The linear sub-system H is characterised by the impulse response h(t) = e −2t , where t denotes time.

    Block diagram is the product of x1(t) and x2(t) going through a block step of h(t) (exp-2t)

    Give a mathematical proof that this is a nonlinear system.

    Question attached in picture.

    2. Relevant equations
    α1y1(t) + α2y2(t) = H {α1x1(t) + α2x2(t)} , condition for linear stability

    where x1(t) and x2(t) are two input signals and y1(t) and y2(t) are the corresponding output signals for system H

    3. The attempt at a solution

    Would my equations become

    y1(t) = x1(t)e(-2t)

    y2(t) = x2(t)e(-2t)

    then calculating one way

    y(t) = α1x1(t)e(-2t) + α2x2(t)e(-2t)

    then the other

    y(t) = e(-2t)[α1x1(t) + α2x2(t)] = α1x1(t)e(-2t) + α2x2(t)e(-2t)

    But that would suggest linearity... Is there something I'm missing?
     

    Attached Files:

  2. jcsd
  3. Jan 26, 2015 #2

    epenguin

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    Gold Member

    You seem to be missing totally that the input to H is g(t) and inventing two outputs y when there is only one.

    Seem. Thisnis not my field but it sure seems.
     
  4. Jan 26, 2015 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Yes, you are missing the effects of "g".
     
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