Now, this is a property that can be shared also by non-linear systems, therefore,

therefore it's a property that I cannot use to prove that the system is linear.

But I can use to prove that the system is non-linear.

And this is a simple example, we can proceed there the system, that

we looked at the previous slide, so using the notation here YN1

is the response of the system to X X as an input, right?

And we define the system as 255 minus X, N1, N2, right?

So, it's like the system takes an eight bit

image and inverts it, finds the negative of it, right?

So clearly if I put a zero as the input of the system, the output

equals 255, hich is different than zero, and therefore this system that

finds the negative of an image is non-linear.

Generally speaking is rather forward to utilize

this homogenize property in this equation that

you see here on top, and prove or disprove that the system is linear.

And this property and everything that we

covered here, this light applies to twodimensional Systems

and signals as well as one dimensional, three

dimensional, five dimensional signals and systems in general.