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## Homework Statement

Hi there, I've been trying to gain some intuition on how the convolution sum works, but as I dig deeper I am realizing that there is an issue with my intuition of signals and systems, in particular the unit impulse response.

My issue is trying to understand how a unit impulse signal can have a system response that is not a constant.

## Homework Equations

For a signal x[n] the output from an lti system is h[n] when the input is the unit impulse function δ[n] .

## The Attempt at a Solution

I am following a textbook (Oppenheim ) and I see in it, and in nearly every online source, that when a unit impulse is the signal then the output is some function h[n] but what I do not understand, is how this output h is not simply one value at one time (like the unit impulse passed into the system)?

Surely if the output of a system whose input was a unit impulse, the system cannot be a time invariant system if the output is a time dependent function!

Since I cannot find an explanation anywhere, and that every source I see seems to never mention this, I am guessing that there is some fundamental misunderstanding that I possesses regarding systems and signals. Would appreciate any guidance!