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Proving a system is LTI based on input and output

  1. Sep 29, 2012 #1
    edit: you aren't proving it's LTI, you proving it COULD be lti

    1. The problem statement, all variables and given/known data
    the question:
    could the following system be LTI?
    x(t)=-5cos(2t) --> y(t)=exp(-2tj)


    2. Relevant equations
    the chapter is about eigenfunctions of LTI systems, wich are of the form exp(st).


    3. The attempt at a solution
    So my guess for what i had to do, was find a transfer function H(s), so that H(s)*x(s)=y(s).
    so i wrote x(t) as follows:
    x(t)=-5/2(exp(2*t*j)+exp(-2*t*j)
    so
    x(2)=-5/2(exp(st)+exp(-st)) with s=2j.

    so than i thought, H(s)=y(s)/x(s), but y and x are still functions of t, so i don't know what to do now...

    and btw laplace isn't explained untill the next chapter so i'm not supposed to use that.

    the given answer is 'yes (H(s=2j)=0)'.
    so i think i do indeed need to do something with the transfer function.
     
  2. jcsd
  3. Feb 7, 2015 #2
    If the output is of the same form as the input but scaled by a constant is that an LTI system? Is the output the same form as the input? (coefficient of sin could be 0)
     
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