# How to make equivalent system using the Noble Identity?

I am trying to get equivalent of this system using the Noble Identities:

$$x[n] \rightarrow \boxed{H(z^L)} \rightarrow \boxed{\uparrow L} \rightarrow y[n]$$

$$x[n] \rightarrow \boxed{\uparrow L} \rightarrow \boxed{H(z^{L\cdot L})} \rightarrow y[n]$$