I am trying to get equivalent of this system using the Noble Identities:
$$x[n] \rightarrow \boxed{H(z^L)} \rightarrow \boxed{\uparrow L} \rightarrow y[n]$$
my answer is
$$x[n] \rightarrow \boxed{\uparrow L} \rightarrow \boxed{H(z^{L\cdot L})} \rightarrow y[n]$$
Is this answer correct?