discrete time signal processing problem

flashist

Joined Jan 15, 2013
2
I'm struggling trying to follow an example, it has the following set of equations:

W$$_{2}$$(z) = $$\alpha$$(W$$_{4}$$ - X(z))
W$$_{4}$$(z) = Z$$^{-1}$$(W$$_{2}$$(z) + X(z)

and converts them into this:

W$$_{2}$$(z) = $$\frac{\alpha (Z^{-1}-1)}{1-\alpha Z^{-1}}X(z)$$
W$$_{4}$$(z) = $$\frac{Z^{-1}(1-\alpha)}{1-\alpha Z^{-1}}X(z)$$

I must have missed something, because I can't figure out how to make that transition. Anyone who would be able to explain? Just one of them should do the trick.

WBahn

Joined Mar 31, 2012
26,398
You got some sloppy notation in your first two equations, such as missing parens.

What do you get if you substitute the second equation into the first and then solve for w2?

flashist

Joined Jan 15, 2013
2
I guess it went away in the tex code mess of mine. I've gathered as much as needing to do that, but whenever I do, I can't get a proper result, winding up with both W2(Z) and W2(Z$$^{-1}$$) and can't find a way of ridding of it.

Last edited:

WBahn

Joined Mar 31, 2012
26,398
How about factoring W2 out from both?

Please show your work, for however far that you've gotten. Otherwise we are just talking in generalities with no idea whether we are on the same page or not.