Well, the title says everything. I know I can find a z-transform, find $H(z)$ and then find a appropriate invert system and comment on that. How do I explain it to a person who does not know z-transform?
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It seems to be a differentiator. Explain that only the difference between successive input signals is output.
Show an integrator that would sum the differences that would restore the signal.
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Does it restore the signal? Seems like it will be off by a constant. – Thomas Andrews Sep 27 '15 at 17:52
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Ah yes, there is a constant at the start that is thrown out by the first operation. So he may require a start at zero. Or an initialization. – Kelsey Bowman Sep 27 '15 at 18:50
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No it is not. Take two different constant functions say $x_1[n]$ and $x_2[n]$. Then their output is the same, zero. Hence the given system $y[n]$ is not invertible.
Pure
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Take $x_1[n] = 1$ and $x_2[n] = 2$ for all $n\in \mathbb{N}$. Both have output $y[n]=0 $. The system cannot be inverted: one output cannot distinguish at least two different inputs.
Laurent Duval
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