# Seemingly no division operation is done of the diagram of the transfer function

Given the below system.

$$y\left[n \right] =2 x\left[n \right] -x\left[n -1\right] +0.5 y\left[n -2 \right]$$

We'll find out the transfer function of it.

So, easiely using z-transform,

$$Y(z) =2 X(z) -X(z) z^{-1} +0.5 Y(z) z^{-2}$$

$$Y(z) \left\{ 1-0.5 z^{-2} \right\} =X(z) \left\{ 2-z^{-1} \right\}$$

$$H\left( z \right) = \frac{Y(z) }{X(z) }= \frac{2-z^{-1} }{1-0.5 z^{-2} }$$

gained it.

Currently I can't get the below diagram.

I can't see component which operates division so it is weird that the diagram is applied to the transfer function.

About the blue domain of below, currently I can't get how the 1 of the denominator of the transfer function is attained.

What I've been missing or what should I study for next?

• I'm a bit confused where you think the division should appear? May 13 at 12:44