Determine if the following system is time invariant: y(t) = x(t - 2) + x(2 - t)

[awelex]

Homework Statement

Determine if the following system is time invariant:

y(t) = x(t - 2) + x(2 - t)

2. The attempt at a solution

I know from the solutions that the system is NOT time invariant, yet whenever I try to solve it I get the opposite result. Here's what I'm doing:

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

x2(t) = x1(t - t0)
y2(t) = x2(t - 2) + x2(2 - t) = x1(t - t0 - 2) + x1(2 - t + t0)

y1(t - t0) = x1(t - t0 - 2) + x1(2 - t + t0)

Therefore y2(t) = y(t - t0)

What am I doing wrong?

Thanks!

 

[NascentOxygen]

You have told us everything you know about x(t)?

 

[awelex]

Yes; no information at all is given about x(t).

 

[awelex]

Any takers?

I found a case that clearly shows that the system is not time invariant, but I'd still love to know what is wrong about my proof. I can't seem to figure it out.

Thanks!

 

[NascentOxygen]

Please return to the specification of the problem, and quote verbatim the sentence there containing the word "odd" or "even".