View Single Post
Old 05-05-2016, 11:32 AM
ntvy95 ntvy95 is offline
Join Date: Jan 2016
Posts: 37
Default Re: invalid points in Z transform

Originally Posted by pouramini View Post
The book says

How a point in Z can be not a valid transform of any x?

I suppose any x will be mapped to a z! not!?
Here is my understanding:

Any x should be mapped to a z, but not any z can be mapped to a x: In other words, nonlinear transform \Phi may not be an onto function.

For example the nonlinear transform z = \Phi (x) = [1, x^{2}_{1}, x^{2}_{2}] (given in the book), if z_{1} < 0 or z_{2} < 0 then there is no x can be mapped to such z because there is no x_{1} such that z_{1} = x_{1}^{2} < 0 and no x_{2} such that z_{2} = x_{2}^{2} < 0.

Hope this helps.
Reply With Quote