Hi I'm supposed to determine if $y[n]=nx[n]$ is invertible.
I found an answer that says that it's not because $x[n]=δ[n]$ and $x[n]=cδ[n]$ (c is a constant) gives the same output.
Could someone please explain why that is?
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There is a lot of information missing here. Could you please elaborate what exactly you mean with invertible? And also, what is the range of $n$? – Manatee Pink Feb 04 '22 at 09:37
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I mean if the system y[n]=nx[n] is invertible. x₁ ≠ x₂ ⇒ y₁ ≠ y₂ or y₁ = y₂ ⇒ x₁ = x₂. The range of n is not specified. – Kickpuncher Feb 04 '22 at 09:59
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Now I am more confused than before. What do the subscript 1 and 2 mean? Do you mean $x$ and $y$ evaluated at two different times? If that is the case, the range of $n$ is crucial. If it contains 0, then it isn't invertible. If it it doesn't, then it is invertible. – Manatee Pink Feb 04 '22 at 10:53