Is $y[n]=x[n]-x[n-1]$ invertible system?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.