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Is $y(t) = \cos(t) + x(t)$ a time-invariant system?


$y(t-k) = \cos(t-k) + x(t-k)$

But it isn't equal to $\cos(t) + x(t-k)$

So, would it be time-invariant?

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You've answered the question yourself already. So, does the response to a shifted input equal the shifted response to the original (non-shifted) input? If so, then the system is time-invariant. Otherwise, it's a time-varying system.

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  • $\begingroup$ It's a time-varying system then. $\endgroup$ – Siddharth Garg Nov 12 at 12:51
  • $\begingroup$ @SiddharthGarg: That's right. $\endgroup$ – Matt L. Nov 12 at 13:36

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