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How does a time delay affect the difference equation of a LTI-system?

Let's call the output of the first system $y_1[n]$ and that of the second $y_2[n]$. It's trivial to see that $y_2[n]$ is just the delayed version of $y_1[n]$, i.e. $$y_2[n] = y_1[n-1] \tag{1} $$ We ...
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