# Proving a system is LTI based on input and output

1. Sep 29, 2012

### robijnix

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. Feb 7, 2015

### jssamp

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)